On most of the E Carib cruises wear a pair of shorts, take a clean shirt for each evening, wear shoes that don't require socks and you will look like everyone else. Underwear is optional. I would think ship's would require luggage like the airlines but the last three day junket I was on I'll swear there were people who lived on the pool deck and left wearing the same clothes, (not much) they got on with.
If you insist on more, check the cruisediva site. She packs everything she owns and then some.