I don't understand your statement that the mission of the CVL is to scout for the cruisers. A CVL was a light aircraft carrier usually built on the hull of a cruiser. (USS Independence) It had the speed to keep up with the fast carrier force and they were fast to build.
I was thinking that what a cruiser squadron really needed was a CVL with scout/recon aircraft to search for the raider{s}. The 9 cruisers sent to hunt down the Admiral Scheer in 1940 were unable to find the raider, they also had trouble using their floatplanes because of the heavy seas in the S. Atlantic
If you are talking about the float planes carried by BBs, CAs and CLs those originally were intended as scouts but evolved into spotters for gunfire and eventually were left off. My reference for Firefly gives the range of around 1000 miles.
I have a range for the Firefly as 1,364 miles, the Hellcat as 1,089 and the Corsair as 1,014.
The Corsair's first combat was on Valentine's day, 1943 but it did not see extensive carrier duty until 1944. Another reason a Firefly would not be looked on fondly by the USN was that it had a liquid cooled engine which the USN had pretty much banned in the !930s. By late 1944 the USN had moved more and more to the fighter bomber with the dive bomber and torpedo plane having smaller contingents on carriers. The reason for this was they needed more fighters to counter the kamikaze and the Hellcats and Corsairs could drop bombs and kill bombers, torpedo planes and kamikazes all in one package.
Yes and that make sense too, because of the high intensity operations in the Coral Sea/Central Pacific, where a carrier might on any day could reasonably expect an air attack of dozens if not 100's of enemy aircraft.
The raiding or hunting CVL would not expect air attack very often, if so it might be 10 - 15 long range bombers. Thats why a FB/Recon aircraft would work, as there would very rarely expect enemy fighters to be present, if there were it would be perhaps 6 - 12 from an enemy CVL.
If your CVL was hunting a single Pocket Battleship for example, the CVL's TB's might handle the job. If however the Germans had launched the raid as planned in the Spring of 1941 it would include Gneisenau, Lutzow Prince Eugen. As events turned out, Gneisenau was bombed by the RAF Lutzow was also unavailable, so it was Bismarck Pr. Eugen that sortied later in May.
If the Battlecruiser, Pocket BB CA had sortied, a squadron of TB/DB's would probably not be able to do the job, {and take heavy losses doing so} so if your "hunting squadron" was a Battlecruiser, a few CA's a few CL's then the job for your CVL would be to find the raiders, and perhaps assist in the battle.
I think if this situation involved the US, it would be in early 1942, where a few Japanese cruisers are sinking shipping around Samoa/Tahiti. The USN can't spare a full size CV, so they send a CVL + a few CA's CL's to hunt down the raiders.