Even a revolutionary fighter manufactured in too large numbers to make this list, the Me-262 (seems to be cut off generally below 1,000, though more Baltimores than that, or Me262's, were produced), didn't really make a big impact on the war in the end. A conventional fighter built in small numbers would have a much tougher time doing so; numbers were pretty important for single engine fighters.
I don't think it's a coincidence that the a/c which naturally appeal as top of this list in importance tend to be large maritime patrol/strike types, because that's a role where smaller numbers could accomplish more.
I would say Fw 200, and the fact that around 1/3 as many were produced as Sunderlands acts in Condor's not Sunderland's favor if you look at the question as relative impact compared to numbers: the Sunderland didn't have 3 times the impact IMO. The Condor affected British stategy in the convoy war noticeably in its heyday and was nearly unique as a German weapon at the time. The Sunderland was one among many types of a/c and other resources going after U-boats in a relatively similar way. But I'd rate it No.2, with the other flying boats like 'Mavis', 'Emily' and perhaps Coronado following it.
After that, the category of British carrier a/c involved in small but not unimportant early campaigns might follow, Gladiator (especially adding in its significant land role in some small scale campaigns), Skua, Fulmar.
The USAAF needed a real night fighter in the Pacific lest Japanese night raids be a more serious nuisance against bomber bases in '44-45 particularly, and P-61 was there; but in ETO the P-61 just added a bit to Anglo-US nightfighter capabilities, and the US itself had less need of one.
I think the poll's initial question is valid, but also agree the follow up line "Some aircraft were built in small numbers but still had a sizable impact on the course of the war." might be an overstatement even for the winner, FW 200.
Joe