I'm no seaman but would NOT sail the Carib without some armament. Shotgun on the boat would be a must for me.
My stagename, Garufa, is actually the name of my good friend's boat that I lived on in the Bahamas for two weeks then sailed over to the US for Summer storage in Chesapeake Bay.
While I'm pretty much Gilligan on a sailboat, my friend, his father and uncle who own the boat do this twice a year and have come across some questionable characters. There are pirates in the Carib just like everywhere else.
You're dealing with international issues so just do some careful reseach. I honestly don't know how carefully they seach boats in other countries but they don't here. A sweet Remmy 870 Marine could easlily be placed under a floorboard or reported and stored depending on whatever Island you go to.
Needless to say, handguns most likely are out of the question.