I believe the Mosquito had a de Havilland manufactured propeller with the blades made from aluminum. With that said, a wood prop may absorb some of the radar depending on the position of the blade. I don't think the spinner is going to help much as it's held on with metal fasteners, and lastly even with wood props you have an aluminum hub which I doubt will be shielded by spinner.
In 1940 with the risk of glider landings the British undertook experiments to see if mostly wooden gliders could be seen on radar, the answer was yes, even after removing what metal they could.
According to the Ministry of Aircraft production most British built Mosquitoes ended up with US built propellers, the longer story follows.
Ministry of Aircraft Production, Monthly Statistical Bulletin which starts in March 1942, Mosquito propeller systems. Note how the data presented changed over time. As far as the Ministry is concerned Mosquito propellers were mostly from America, and when British made propellers are mentioned they usually do not give a type/model number.
March 1942
The propeller blade deliveries table starts in January 1941, wooden blades start in November 1941. Metal blade forgings are from De Havilland and Rotol, with De Havilland dominating the output. Propeller for Mosquito is the Hydromatic De Havilland including the constant speed unit.
Repaired propellers are categorised as Fixed Pitch Wooden, Fixed Pitch Metal, Two Pitch, Constant Speed Cam, Constant Speed Hydraulic De Havilland, Constant Speed Hydraulic Rotol, Constant Speed Electric (but none until March 1942), American two pitch, American Cam, American Hydraulic, American Electric, first US propeller repairs in July 1941.
April 1942,
Blade deliveries table now has factory information, De Havilland Lostok producing in January 1941, Stag Lane began production in July 1941, Wooden blades by Rotol. Blade forgings, De Havilland are Dural, Rotol are Dural (starting February 1941) and Magnesium, Fairey fixed pitch Dural from January 1941. Thrust bearing (blade sets), De Havilland and Rotol from January 1942, Wooden blade root adaptor production begins in November 1941.
Hub forging and Weldings, De Havilland Cam Spiders and Cam Barrels, Hydromatic Spiders and Hydromatic Barrels from January 1941. Rotol Hydraulic 3 blade forgings from January 1941, Weldings from December 1941, Hydraulic 4 blade, 198 forgings produced to end February 1942, 58 Weldings in March, Electric forgings from April 1941.
Repairs now amalgamate the British Two Pitch and Constant Speed Cam figures, plus the American Two Pitch and Cam figures.
August 1942,
Propeller Hydromatic, De Havilland 3 Blade, for Mosquito B.IV, F.II and T.III, plus constant speed units.
Rotol ceases Magnesium blade forging production.
Barrel Set delivery figures recalculated, previously they were unmatched "front" and "rear" barrels. USA 3 blade hydraulic forgings have been in figures since January 1942, broken out as a note to the table for the first time in August.
September 1942
Propeller Hydromatic, De Havilland for Mosquito B.IV, F.II and T.III, plus constant speed units.
Propeller Hydromatic, De Havilland 4 Blade, for Mosquito PR.VIII, B.IX, F.X/FB.XI, plus constant speed units, there is an entry but no production this month.
Table for Propeller stocks at Aircraft Contractors or awaiting repairs added. Table for Constant Speed Unit stocks at Aircraft Contractors or awaiting repairs added.
Table for New Propeller production by types added, from June 1941, Fixed Pitch Wood, Fixed Pitch Metal, Constant Speed Cam, Constant Speed Hydraulic De Havilland, Constant Speed Hydraulic Rotol 3 Blade, Constant Speed Hydraulic Rotol 4 Blade (from November 1941), Constant Speed Electric..
Table for New Propeller production by firms added, from May 1941, firms are De Havilland Stag Lane, De Havilland Lostock, Rotol No.1 Shadow (production from July 1942), Fairy (production from June 1941), Horders Richmond (production from June 1941), Bath Aircraft (production August 1941 to April 1942, then a pause until October), Airscrew Company (production from June 1941),
Table for New CSU production by firms added starting in May 1941, De Havilland Cam, De Havilland Hydromatic, Rotol 3 Blade, Rotol 4 blade (from December 1941), Electric
Table for Assembly of USA propellers in UK added, data starting in December 1941, Stag Lane Warwick I, Lostock Lancaster I from July 1942, Stag Lane Stirling II from September 1942.
October 1942
Hoover added to firms producing propellers, first production in October. Bath Aircraft resumes propeller production. Fairey fixed pitch Dural blade figures from January 1941 deleted as inaccurate. Rotol ceases Dural Blade forgings, except for a batch October/November 1943.
November 1942
Assembly of US propellers is now cumulative totals, with 122 for Mosquito at Lostock, versus 411 Mosquito built to end November.
After being dropped in October Propeller Hydromatic, De Havilland 4 Blade, for Mosquito PR.VIII, B.IX, FB.X, PR.IX, NF.XIV plus constant speed units entry reappears but no production this month (2 produced in December)
December 1942,
New CSU production table is now De Havilland Cam, De Havilland Hydromatic small, De Havilland Hydromatic large, Rotol Hydraulic Feathering, Rotol Hydraulic Non Feathering, Electric.
January 1943,
Assembly for USA propellers has CSU data added. Table for delivery of Propeller Hub Forgings and Hub Weldings dropped.
Production of New Propellers for the Month drops Mosquito 3 blade entry, adds type field, Hydromatic, De Havilland 4 Blade, for Mosquito PR.VIII, B.IX, FB.X, PR.IX, NF.XIV type D1/445/1
Production of Constant Speed Units for Month adds type field, Small Hydromatic De Havilland, Mosquito B.IV, F.II, T.III type AY105, Small Hydromatic De Havilland, Mosquito PR.VIII, NF.XV type AY113
Propeller Stocks include 90 Hamilton for Mosquito F.II, B.IV, NF.XII and FB.VI from 395 US Propellers assembled for Mosquito.
February 1943,
Constant Speed Cam propellers redesignated Constant Speed Bracket. Vickers Armstrong now making propellers. Propeller Stocks include Hamilton for Mosquito F.II, B.IV, NF.XII, FB.VI, T.III
New Table, CSU production by firm, starting in December 1942, De Havilland Stag Lane, Rotol Gloucester, Rotol Worcester, Standard, Gillette, No. 1 Shadow.
Constant Speed units now include Double Acting De Havilland for Mosquito B.IX, PR.IX, FB.X, NF.XIV and Welkin, type AY201, but no production, in fact no production until May 1944.
March 1943,
CSU by firm revised, De Havilland types made by De Havilland and Standard, Rotol types made by Rotol Gloucester, Rotol Worcester, Standard, Gillette, No. 1 Shadow.
Constant speed unit type AY105 now for Mosquito IV, F.II, T.III, FB.VI and NF.XII. Hydromatic, De Havilland 4 Blade, now for Mosquito PR.IX, FB.X, NF.XIV type D1/445/1
April 1943,
Propeller Hydromatic De Havilland 3 Blade for Mosquito NF.XIII type 45/2. Hydromatic, De Havilland 4 Blade line deleted. Spinner production table added, Hydromatic De Havilland 3 Blade for Mosquito NF.XIII, second line for Mosquito F.II, B.IV, FB.VI, B.IX, PR.IX, third line for Mosquito T.III
May 1943
Two new tables, starting from November 1942, Spinner production by type, De Havilland Bracket, De Havilland Hydromatic 3 blade, De Havilland Hydromatic 4 blade, Rotol Hydraulic 3 blade, Rotol Hydraulic 4 blade, Rotol Hydraulic 5 blade, Rotol electric.
Also New Spinner production by firm, De Havilland types C.S.A, De Havilland types Sankey, Rotol types Rotol Gloucester, Rotol types C.S.A., Rotol types Sankey.
Production of Spinners table entry added for Hydromatic De Havilland 4 blade for Mosquito PR.IX, FB.X and NF.XIV, 2 produced in May.
June 1943,
Standard added to firms making propellers, first production in June. CSU Stocks include Hamilton HAY154 for Lancaster I, III, Mosquito FB.VI. Rotol produces its first 5 blade propellers and 5 blade spinners, then a pause in production until September.
July 1943
New type of propeller being made, the Rack. Constant speed unit type AY105 now for Mosquito B.IV, F.II, T.III, B.IX, PR.IX and NF.XII, type AY111 for Mosquito NF.XIII, Double acting type AY201 for Mosquito B.IX, PR.IX, FB.X, NF.XIV, Welkin I, York I Propeller Stocks include Hamilton for Mosquito F.II, B.IV, FB.VI, T.III, B.IX, PR.IX
October 1943,
Mosquito B.XVI propeller Hydromatic De Havilland 3 blade type 45/2, Mosquito NF.XIV propeller Rack De Havilland 3 Blade. Constant Speed Unit AY105 for B.IV, F.II, T.III, B.IX, PR.IX, AY118 for Lancaster I, III, Mosquito B.XVI, double acting De Havilland type AY201 for Mosquito NF.XIV plus Welkin (Small contra)
November 1943,
Propeller Hydromatic De Havilland 4 blade for Mosquito NF.XV type D1/445/1. Propeller Stocks include Hamilton for Mosquito F.II, B.IV, FB.VI, T.III, B.IX, PR.IX, NF.XIII. CSU Stocks include Hamilton HAY 154 for Lancaster I, III, York I, Mosquito FB.VI, T.III, NF.XIII, B.IX, PR.IX
January 1944,
Propeller Rack De Havilland 3 Blade for Mosquito NF.30, 3 produced, also double acting CSU AY201 for Mosquito NF.30, none produced. Standard ceases propeller production.
March 1944
Templetons is added as maker of De Havilland propeller blades, staring in January 1944, in April 1944 the report has Templetons production beginning in May 1942, previously counted under Lostock.
April 1944,
CSU unit AY118 for Lancaster I, Mosquito B.XVI, PR.XVI, FB.VI, NF.30. USA propellers for Mosquito also being assembled by Standard at Coventry. Rotol Gloucester ceases CSU production.
May 1944,
Spinner Hydromatic De Havilland 3 Blade mark list has by now become FB.VI PR.XVI, B.XVI, NF.XIX, NF.30. CSU Double acting De Havilland for Mosquito B.XVI, PR.XVI, NF.30 type AY201, first production of 20, another one made in October. Shadow factory No.1 ceases CSU production.
June 1944
CSU Small Hydromatic De Havilland for Lancaster I, Mosquito B.XVI, PR.XVI, FB.VI, NF.30, T.III type AY118, AY119. CSU Double acting De Havilland for Mosquito B.XVI, NF.30, PR.32, Hornet type AY201. Propeller stocks add a by type field, stocks include Hamilton A5/147 for Mosquito F.II, B.IV, FB.VI, B.IX, PR.IX, NF.XIII. A5/126 for Mosquito T.III. A5/146 for Mosquito FB.VI, PR.XVI, BF.30, T.III
July 1944
CSU Small Hydromatic De Havilland for Mosquito B.XVI, PR.XVI, FB.VI, NF.30, T.III type AY119. Rack propeller production ceases.
August 1944
Rotol begins production of 2 blade hydraulic constant speed propellers. Hordern Richmond cease propeller production until December.
September 1944,
US propellers assembled for Mosquito cumulative total is now 6,860 versus 3,405 Mosquito built. As has been the case for some time there are no reported stocks of or under repair British propellers for Mosquito. Though Hydromatic De Havilland 3 blade propellers type 45/2 for Mosquito are being made, and Hydromatic De Havilland 4 blade (no model number given), along with AY119 CSU. CSU unit AY121 for Mosquito NF.XIX. Bracket propeller production ceases as does CSU units for them.
October 1944,
Propeller stocks include Hydromatic De Havilland 3 Blade type 45/2 and Hydromatic De Havilland 4 Blade type D.14/445/1 for Mosquito. Number 1 Shadow factory ceases propeller production. Assembly of US propellers now gives model numbers, for Mosquito, at Standard A5/146 or 160, at Lostock A5/146 or 160 and A5/163.
November 1944,
Hydromatic De Havilland 4 Blade for Mosquito type 445/1. Cumulative totals of US propellers for Mosquito give type as A5/126, A5/146, A5/147, A5/160, A5/163 with CSU HAY154.
December 1944,
Mosquito F.II. B.IV, FB.VI, B.IX, PR.IX, NF.XIII, B.XVI Hamilton A4/147, Mosquito FB.VI, PR.XVI, NF.30, T.III Hamilton A5/146, other Mosquito Hamilton A5/160. Rotol ceases 3 Blade Hydromatic constant speed propellers.
January 1945,
Mosquito B.XVI, FB.VI, PR.XVI, NF.30, T.III Propeller Hamilton A5/146 or 160, PR.34 A5/164 or 165, B.IX A5/163. Hoover ceases propeller production.
February 1945,
Mosquito 33 type AY118 CSU, Mosquito and Lancaster Hamilton 4G8-G22J or G26J CSU
March 1945,
Propeller stocks include D.1/445/1 for Mosquito PR.34, B.35 and NF.36 Double Acting CSU monthly production begins (20 have been built in May and 1 in October 1944)
Gillette CSU production ceases as does electric CSU production since Gillette was the sole UK maker of electric CSU.
April 1945,
Mosquito FB.VI, B.XVI, PR.XVI, NF.30, PR.34, T.III CSU AY119, AY122. Contra rotating propeller production begins. CSU AY202 stocks for Hornet, Sea Hornet and Sea Mosquito, the latter also using AY118. AY202 production was for Lincoln II, Sea Mosquito 33, Hornet F.I, Sea Hornet F.XX.
August 1945
Large Hydromatic De Havilland type AY122 CSU units for Lancaster I, VII, York I, Mosquito FB.VI, B.XVI, PR.34, B.35, NF.36. Double Acting De Havilland type AY202 for Lincoln II, Sea Mosquito 33, Hornet F.1, Mosquito PR.34, B.35, NF.36 Stocks reports discontinued. Vickers Armstrong cease propeller production. To end August 1945 12,211 US propellers assembled for Mosquito, types A5/126, A5/146, A5/147, A5/160, A5/163, A5/164, A5/165
September 1945
Double Acting De Havilland type AY202 or 203 for Lincoln II, Sea Mosquito 33, Hornet F.1, Mosquito PR.34, B.35, NF.36. Fairey and Hordern Richmond cease propeller production. Electric propeller production ends? US propeller table dropped.
October 1945
Sea Mosquito TR.33 propeller Hydromatic De Havilland 4 Blade type D14/445. De Havilland 3 blade, hydraulic constant speed propeller production ends? And De Havilland large Hydromatic CSU unit production ends?