There is normally a "squirrel season" in areas. So check the game laws for hunting. If squirrels have no bag limit, then you might be fine.
Nov 4- march 7 seems to be the Florida squirrel season? 12 per day(possession limit 24)
Prohibited methods for taking game do seem to include traps. But "furbearers" can be trapped using live traps.. are squirrels "furbearers"?

http://myfwc.com/docs/RecreationActi...egulations.pdf

I think that since squirrel is considered a game animal, the laws regarding hunting takes full precedence. But this is all just my best guess. Trapping squirrels to use as food may indeed be prohibited, even if they are nuisances.