Realizing this is an old post, I won't go into great detail. We visited the Caymans several years ago. Since Grand Cayman is pretty commercialized, we decided to look at Little Cayman or Cayman Brac. The travel adviser we talked to had the islands switched around. She told us there was no fishing on Little Cayman so we booked a place on Cayman Brac. There is one beach on Cayman Brac and apparently there is one fellow who does some guiding. It was not the right time of year to find any bonefish but I can see that there may be some limited opportunities there. Much of the island is not appropriate for flats fishing but you could probably catch some barracuda. Contrary to the advice we got, Little Cayman has some good flats areas but you may have to stay at a more expensive place since lodging is limited. It also supposedly has some tarpon in landlocked lakes.
All in all, I suggest you would be better off going to Cozumel. Hire a local to fish to great flats on the north end of the island. I caught 5 bonefish the very first time I tried fishing for them on these flats. I also missed a big snook due to my inexperience. It is a largely undiscovered area but can't take lots of traffic. Treat it gently if you go. There is also lots of other things to do on Cozumel. It's a small island so crime is not a problem like it is across the water in Cancun.