It sounds like a wonderful cruise itinerary! I think that comfortable casual will be fine. It will be lovely in both London and New York in August - New York can be humid and warm, and London's climate is much like Seattle's climate. If I were you, I would take a bit of everything from shorts to a sweater and jacket - just to be prepared. You should be able to swim and the weather should be comfortable, summer temperatures. There might be some windy and/or cloudy days that would not be good days for swimming, but I think that you can assume that most days will be fine and comfortable, too.