No, Hickok would not have carried that.
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https://news.yale.edu/2015/07/21/gunfights-us-colonialism-and-studying-american-west-east-coast
That picture is of a .44 Lefaucheux type pinfire revolver. Since it's unmarked, it's probably made in Belgium. It is decidedly inferior to the Colt revolvers of the day, both in workmanship and in cartridge power. Hickok usually carried Colt revolvers (although I think he did own a S&W) in a sash, butt-forward for a reverse twist draw.
Hickok may have given it away, but I can assure you he never carried it.
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The shootout launched Wild Bill’s fame as a gunman. He went on to have a short-lived career as a lawman in Kansas, befriended other renowned figures of the Wild West such as Calamity Jane and Buffalo Bill Cody, became a dime novel hero, married a circus proprietor, and continued his gambling career.
Bill, you had me at "married a circus proprietor".
