To clarify about the ID requirements...
Local port security wants to see a photo ID plus the cruise card. It depends on the port as to whether this happens, but it will happen in most Caribbean stops. The ship itself will only need the cruise card which you use to 'card in' and 'card out' of the ship at a security station that shows your photo when your card is scanned. This photo will be taken on embarkation day, either at check-in or as your board the ship for the first time. It is tied to your cruise card electronically.
The usual scenario is port security will have people stationed at the pier to check guests returning to the ship. In Jamaica the local police are more intrusive than in Grand Cayman. They may also want to search all packages, bags, and even pat down passengers. Drugs are the big issue. You then move on to the ship where you get further screening by ship's security where they scan your cruise card and x-ray all packages, backpacks, etc., and each guest goes through a metal detector. It is quick and usually only takes a minute.
The ship will tell guests what the local requirements are prior to your leaving the ship. Bottom line is that even if a photo ID isn't required, it is foolish to go ashore without one.