We did a Panama Cruise with Viking, who also have a reasonably dressy dress code, carry on only and it was fine. I bought a couple of light dresses that packed up small, and we did laundry on the trip to keep the clothes fresh. Hubby didn't bring a jacket, which Viking didn't require, so that would be one item to add, but otherwise, we managed fine.
We are doing Cunard out of Vancouver in August...no flights for us, so going to take my biggest suitcase!