I go to the bahamas quite regular, and it is very difficult to leave with things from the ocean. I was snorkeling on a different island there and found some cool shells, and big starfish. I snuck away some shells, but was told not to get caught or I would be fined. However you can buy whatever you want from there and bring it home with no problem..'
that is just my 2 cents
Even if you could get stuff out of that country, your sure as heck aren't getting it into this country, with out proper permits (CITES, US F&WS, Customs, etc).