I wish I could advise you on this question from personal experience, but I've never been at sea for more than 8 days at a time. My immediate thought is that I would only want to take a cruise like this on a ship that has self-service passenger laundries, otherwise your cleaning bill could cost as much as a few shore excursions! My advice would be to pack about two weeks worth of mix-and-match, versatile outfits. Limit your "dry clean only" gear to formal wear. And leave a bit of room in a suitcase for those inevitable purchases along the way.
What a wonderful dilemma to face! Enjoy the experience.