Even though your cruise is to the Caribbean, people will wear typical New Year's eve finery; silk, satin, beads, velvet, strapless or thin straps, long sleeves, short or long gowns/dresses, pants ensembles, etc. It is often cool in public rooms on board ship. The evenings activities are usually all in side. You will appreciate your long sleeve outfits. The only evening/seasonal accessory may be your shoes. Strapy sandals will work well.