Most ports on cruise do not require you to carry you passport when off the ship. Some do, and the cruise line will inform you as to when you are going to one of those. Usually via announcements in the daily Navigator, and the Cruise Director will mention it during the pre-show talk.
To debark the ship you all need your KTTW cards. To get back on the ship, you'll need (in most cases) your KTTW card and (for those 18 and over) a photo ID. That can be a driver's license, or passport, if you have no other photo ID. The photo ID is primarily for gaining entrance to the port area.
Towels are proved at
Castaway Cay - there is a CM handing them out after leaving the ship:
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Can't speak to whether Atlantis has their own towels for you to use.