Dames at Sea is NOT an "old-fashioned sailor" show. It's a spoof of Busby Berkeley movies of the early 1930s, that happens to end with a show-within-a-show staged on a battleship after an earthquake destroys their theater. (Yes, it's a broad comedy.)
The characters aren't actual sailors, but show biz types.
If you want a comparison, look to 42nd Street (not OTT); Dames at Sea tells the same story (star gets injured, chorus girl goes on in her place and becomes a star). The joke is it does it with cast of six rather than a cast of thousands.
The songs are lovely and often hilarious and the overall affect is charming. HOWEVER, its jokes do depend on a knowledge of Busby Berkeley and Ruby Keeler, et al. Do folks still watch those old movies on TV?