I have a bad habit of trying to "date" a movie by the guns I see in it

The revolver issued to Jim by Stein at the beginning of his upriver mission appears to be an American double-action, side swing-out cylinder revolver (possibly or probably a Colt) of a type not in common use till the 1890s.

The one he seizes from "Gentleman" Brown on the river ferry and throws overboard (to Brown's obvious dismay) looks like a Smith & Wesson double-action "hand ejector" type not introduced earlier than 1896, I don't think. So, if I'm right on my gun history, and these clues mean anything, I would date the story to the late 1890s, or maybe about 1900.