Yes birkett is right princess are less bothered,we have just returned from our princess cruise and although a lot of men wore a tux some only woore a dark suit whilst a few wore just a jacket and tie,and although this was europe,i did hear an american gentleman say he thought less men wore a tux in the caribbean,either way as long as you don't go in your jeans or shorts i am sure you will be fine,just enjoy yourself.
Been on the Sun Princess in the Caribbean (excellent)
I do not possess a tux and wore a dark suit without feeling in any way out of place
Having done a few American lines I found that they are less bothered about formality and I have seen people with out a jacket or tie going to a formal night without difficulties.
You may wear a tux or day suit - on three previous Princess Cruises we saw men wear both.
I was on the sea princess in april we had three formal evenings gents were dressed either in tux or dinner suit ladies dressed in long or evening gowns i loved dressing up i to am going back on the sea princess on 10th october for 3 weeks cant wait you will enjoy the ship crew and food excellant take care .