I remember watching an old black and white comedy with my mom when I was younger. I don't remember much. I remember that it seemed to be about a naive American woman who was married/engaged to an SS officer, who was rescued or kidnapped by an American war reporter. I clearly remember one scene from the end of the movie where a Nazi falls off a ship into the ocean, and the crew starts to go back for him, but decide to ignore it after finding out he was a Nazi, lol.
That would have to be Once Upon a Honeymoon (1942), starring Ginger Rogers as a gold-digging woman who marries an Austrian baron and Cary Grant as a reporter investigating the Baron's suspect connections. There is one slight difference from your recollection: the captain calls off the rescue at the end not because of the Baron's politics, but because he is told that the Baron couldn't swim.