My biggest (un-obvious) tip if you wash clothes in the sink, squeeze/wring out the wet clothes in a towel before hanging. It will dry a lot faster. Other than that the obvious is to bring clothes that dry fast. I realize this is harder on a cruise for dinners, events, etc. so that's more of a personal decision.
Some ships don't have laundry facilities, so if you don't want to wash in the sink or send out for the cruise to do it (cost, special handling), you will need to make some sacrifices.
We one-bag carry-on backpack (< 35L) travel so pack all quick dry clothing. Never done it for a cruise but will be my first try in August as we'll be traveling around by train in Spain for 2 weeks before a cruise. Plan is to pack pants, polo and shirt (all quick dry) for dinners. So yes, it'll just be a shirt and tie for me on formal nights.