We are European vacationers, not primarily cruisers, but are doing a Baltic cruise for the convenience of travel between ports. Actually, if you want to be a prime target of pickpockets and stand out as an Ugly American anywhere in Europe, do by all means wear shorts and jeans!
The Baltic ports are all cities -- city attire is proper. That means slacks and non-logo shirts. Good comfy walking shoes (walking sneakers will pass).
Your casual Carribean cruise attire is not appropriate for European travel.
Just back. Had a great time. Only took 2 pairs of shorts. Wish I had taken more. It was very hot-- 90+ Everyone wears jeans and shorts. Only business people dress conservatively. Sundresses are also a must. Only places wear you must cover shoulders and knees are in cathedrals.