We are going on ncl Jewel this August to the Baltic Capitals. We understand ncl to be casual with no dress code and flexi dining times, but it sails from Dover.
Most cruise lines that operate from Southampton encourage "Dressing Up" a few times during the cruise. I personally don't know why some people associate dressing smartly with not having fun or a good time? It is one of the best things about a good cruise to many, including me! The type of thing you are looking for is mainly based in the Med and does not tend to cover Northern Europe. NCL is probably the closest you will get to it sailing from this area to the destinations that you want to visit. Although the Norwegian Jade will be cruising from Southampton shortly, she will be going to the Fjords rather than the Baltic. From what you say, I think that the Norwegian Jewel sailing on regular Baltic itineraries from Dover would probably be your best bet. Happy cruising.