I'll chime in with some others; Very likely not gonna happen. Not with a bike. Ocean water and salt will eat your bike alive and in any case, there's really no need for a bike on those islands—they're far too small to tour on. You could walk most any of the Caribbean Islands in less than a day. Where does one stow a bike on a 30-40-50 foot boat? On deck. Not practical. I've seen folding bikes come off of a boat or two and they're pretty much solid rust.

Learn to sail. It's a means and end all unto itself. You won't miss your bike and you'll have adventures aplenty. Sailing is touring.