Formal night varies from line to line. We cruise Holland America and their formal night is truly formal. But, I have worn cocktail dresses and not long gowns and that was acceptable. If people do not care to dress formally, that is their choice, but they are not allowed in the dining room. However, they can go to any of the other restaurants. We no longer want to do formal so we choose to be casual as do many people. I would call the line you will be cruising with and see what their idea of formal is. Many lines have no formal nights at all.
Keep in mind that even though you will be in the Caribbean, the ships are air conditioned and at night on the water it's cool - so I would bring a pashmina or something to wear at night. During the day it's not a problem. Clothing during the day is shorts/capris & bathing suits. All of the islands are very casual, so again, shorts, etc. are just fine.
Congratulations on your upcoming wedding. You will love the cruise and hopefully it will be the first of many.