I can tell you that indian citizen with american visa (H1b work visa - multiple entry) doesn't require visa for jamaica, cayman island and mexico... I did the caribbean cruise last week... I am quite sure chinese citizen would fall in same category... At the ports of call, all you need is the cruise sailing card which has your name on it plus a photo id... Passport, driving license, even a credit card with your photo on it works... There is no immigration procedure for cruise ports... When you board the cruise from usa... They check that you have multiple entry visa for usa... So that you can enter back... That's it... Then you don't need passport for rest of the trip... That's atleast true for jamaica, cayman island and mexico... Don't know for eastern or southern caribbean...
