I just received an article about Charlie Kendall and the P-40F. One of the photos shows a P40 on a port cat about to be shot off the carrier.  The article connected to the rear of the plane is NOT a tail hook, but a hold back, used to keep the cat from launching the plane until the then hydraulic pressure launched the aircraft.. Once launched, that device actually breaks in half, allowing the cat to shoot the plane off the deck. The US Navy launched dozens of P40s and P47s this way as a way to rapidly deliver flyable aircraft for the USAAF in the SouWesPAC (New Guinea) as well as Spitfires to Malta..

The only USAAF planes tested for Carrier landings were the B25 (PBJ), P51D, and P-39.  Not sure what the Brits did, but they were more curious. 

Here is an interesting link to the Navy' testing of a swept wing p-63, no carrier tests though
http://thanlont.blogspot.com/2011/04/bell-l-39-wing-sweep-evaluation.html

Do a google search of "original sea hawk vernon rabbetts". You will find a colorful account of British carrier trials for the P-40.