Take what is call business casual but bring sweats /gym stuff if you plan to use the spa. I sometimes wear sneakers with my kakhis to do laps on the deck and they do get slick if the sun isn't shinning. Swaters/light jackets would be good especially in the evening..twin sets are good.
We did a crossing several years ago on the Vistiaford, now the coriona,. The trip ended in thecarbbiean so people were in shorts, swimsuits but the staff was on top of the proper attare in the dinning room. Cover ups at lunch and ties etc at time.