I guess it depends on where the cruise ship will dock.

It is not that hard to get tourist visa to those caribbean countries. It is to your friend's best interest to check with the cruise company or the travel agency. I haven't been to a caribbean cruise. so I don't know how strict the cruise companies are at boarding time. Technically speaking, carrying a chinese passport without US greencard will definitely be required to have visa documents to all the countries on the cruise itinerary.