A wise friend of mine once said "pack what you think you need for a cruise - and then remove half of it". He was correct in my case, as we always seem to have clothing that we never wear during the cruise - and we have been cruising for going on 14 years!
Caribbean cruises can be surprising in that the nights can be cool, which is especially true in February. As others have said - a shawl, a rain jacket, a sweater or two - these should get you through just fine. Days will typically be t-shirt and shorts weather, but if a rogue shower and some wind show up, you will be prepared!
Princess is a great cruise line, by the way. One thing I like, among many things, is that Princess uses fresh water in their swimming pools. Most other lines use salt water.
Please let us know how your cruise went. I know I would like to read a review!