My friends and I play an advanced A&A type game in which the carrier air is differentiated by its range instead of by actual vehicle (though there is an exception to that in that the UK has an early war naval fighter unit to symbolize the swordfish/gladiator planes).
This represents the differences that come with the design limitations placed on carrier air.
Now it must be explained that all air units operate a bit differently in that they have a range instead of a movement allowance. You can fly up to the range out to a target, then the range back from the battle. Ranges are 2,2 for fighters and stukas/sturmoviks and 3,3 for bombers. Western Allies also have heavy bombers have that can fly 4,4, but only when doing strat bombing.
Carrier air only have a 1,1 range, but understand that in this game the CV moves first, then the air unit can fly off of the deck to do its combat. There is still the switching out of the generic fighter unit (with the exception of the UK unit until the spring of '42 when the regular fighter can then land on their carriers) from land to CV and vice versa, but the limitations concerning range during an actual attack does model the limits that were present in the war.
I did come up with with a naval air unit for the US and Japan to be used in this game, but it was more of an attempt to power down the generic fighter and its attack value against surface naval units rather than an attempt to come up a unique figurine for differentiation.