Wow, way to beat a dead horse.
Oops yeah I’ll drop it. The West is my passion.
Bat Masterson famously wore a derby on TV, but any resemblance to what he really wore would be purely coincidental.
Brian
“You’re telling me the song isn’t historically accurate?” 
That’s true, and i made that point- the classic Stetson came in late, but what they are wearing is wide brimmed wool hats.
More like a couple of inches and the style- the short brim is turned up in the bowler. Still, I have not yet seen any period photos of working cowboys with bowlers.
As I understand it, the “Cowboys” were a bunch of cowboys. Made a name for themselves by being dickheads. The ordinary ranch hands and cattle drovers weren’t “cowboys” until the press adopted that term.
Not being curled, it can be bent up, or bent down. Bent down, it merges into the ‘bucket hat’ worn by Inspector Clouseau - the ridiculous derivitive of the Sherlock hat.
The English word cowboy has an origin from several earlier terms that referred to both age and to cattle or cattle-tending work.
The English word cowboy was derived from vaquero, Spanish for cowherd or cattle-herder,[3] from vaca, meaning “cow”,[4] and the suffix -ero used in nouns to indicate a trade, job, occupation, profession or position;[5] itself from the Latin: vaccārius, which means cowherd,[6][7][8][9] from vacca, meaning “cow”,[10] and the suffix -ārius used to form nouns denoting an agent of use, such as a dealer or artisan, from other nouns.[11]
“Cowboy” was first used in print by Jonathan Swift in 1725, and was used in the British Isles from 1820 to 1850 to describe young boys who tended the family or community cows.[12][13] Originally though, the English word “cowherd” was used to describe a cattle herder (similar to “shepherd”, a sheep herder), and often referred to a pre-adolescent or early adolescent boy, who usually worked on foot. This word is very old in the English language, originating prior to the year 1000.[14]
By 1849 “cowboy” had developed its modern sense as an adult cattle handler of the American West. Variations on the word appeared later. “Cowhand” appeared in 1852, and “cowpoke” in 1881, originally restricted to the individuals who prodded cattle with long poles to load them onto railroad cars for shipping.[