[A Navy Vet]

IIRC, the term "cowboy" didn't exist until the Earp/Clanton feud in Tombstone. It was a derogatory term associated with the Clantons/McLaurys who would cross the border and steal Mexican cattle. It's well documented in many books, writings, and court documents. BTW, they didn't wear red sashes like in the movie Tombstone. They were known to where sombreros, most likely to facilitate their theft of Mexican cattle.

The original terms were: drover, wrangler, cow-puncher, cattleman, and cow-herder. I could be wrong.

[Rockpile]

There is a Washington Irving story @ 1830 where he writes
of passing “cowboys” driving cattle to market in New York state.
It might even be a word used in England originally.