Sadly I never got that far.
Originally I had thoughts of doing the publicity shot costume with hat, duster, and rifle (and, oddly, the Bowie knife shoved under his belt rather than in its sheath)
but I decided to stick with the simpler costume he wears throughout the film.
I did some research into that quite rare rifle and talked to a couple people who make 3D printed and cast resin replica firearms but that didn't get anywhere.
What I did acquire was an old 1:1 scale plastic model kit of a Winchester rifle which Quatermain shoots at one point in the film. That would have made an ideal prop, lightweight and nonferrous. I always keep in mind practical matters of cosplaying at Cons like getting through Security and not having to carry around a bulky or heavy prop all day.
But then that incident at the Phoenix Comic Con happened and all the Cons here in California banned anything resembling a weapon, even Nerf guns, water guns, Harry Potter wands, etc so even that plastic Winchester wasn't going to work.
I have a really nice replica Colt Python for my Chief Jim Hopper cosplay but I've never tried taking it to a Con.
I have a resin Webley Green for Quatermain but I've only used it for photos I've taken in my garden.