Interesting question. I'm not sure when the term was first used, but it probably dates back to WW2. I have an old Popular Mechanics magazine from the early 50s that usues the term to describe a spearfishing club in California.These were UDT (underwater demolition teams) Navy veterans from WW2. The same magazine issue has an article about a strange new automobile that was about to be imported for the first time into the US: Volkswagen.
The term 'skindiver' seems to have been meant to describe people who dived without the heavy diving suits of commercial divers. They dived before neoprene suits were developed, just wearing trunks: skin divers. When the French invention of Self Contained Underwater Breathing Apparatus came along after WW2, SCUBA became the term for that equipment. Eventually it became the name of the activity itself. The earliest relevant magazine was 'Skin Diver', 1951 or 52 I think, and it was mainly for and about breath hold spear fishermen. As scuba equipment began to become more popular, especially after neoprene suits became available, that magazine retained its name.
The term Skin Diver is older than Scuba Diver, and became part of the language because of the TV show. I was a skin diver as a little boy, 8 years old. No snorkel, no fins, just a basic mask. The other stuff came later. I still, deep down, think of myself as a skin diver. Thanks for forcing that trip down memory lane. If you don't know how you got here, you don't really know where you are. That opinion reflects, I suppose, the fact that I spent more than 30 years teaching History.