Well, from the sound of it, it isn't him being away during Christmas... and it's not about the family he would be going with. From what I read, your real concern was the safety of the ports and the fact that your DS is older than his friend, i.e., there's a little more responsibility on his part.
With that in mind, I would say no. If Jamaica has scared me enough that I wouldn't even go back myself, I would have a really hard time letting my kid go by himself at that age.
Or maybe, you can speak with the family he would be going with and express your concerns. Maybe, they'll already be thinking about the safety of the ports and or maybe you can get a read of their plans at the ports.
I wouldn't be worried about an earthquake because it's just as likely to happen at home than at sea, and he would be safer at sea anyway.