You could also ask to go with another like minded man and agree beforehand to help each other avoid doing things your wife would be hurt by if she knew.
That would make it even easier to find and befriend other ladies, as lots more women travel with their girlfriend. So two guys that are friends kinda helps prove that you are safe instead of "on the prowl" and 2 on 2 introductions are easier than 1 on 1 or 1 on 2, IMO.
I've cruised with 4 other guys, even though 2 of them were enough different than me that we didn't stick together except for dinner. One wasn't even interested in befriending anyone much.