If you're on Ambergris Caye the only thing you're likely to catch is sunburn. You'll get bitten by sandflies around dusk, but I've never heard of anyone catching anything from them. And although I don't drink tap water (don't like the taste) lots of people do and I've never heard of anyone catching anything.
But do use commonsense. Make sure you're protected against Tetanus and Hep A/B. No need for anything against Malaria on the island, or even most places inland. Do try to avoid getting bitten, though.