I have a similar issue with the strap from my Great Grandmother's case for her Polaroid The 800 camera, but haven't done anything yet.
Presently, it's more like a family heirloom, and hadn't been used since the late 60s, early 70s. Since 2012, though, I've used it a few times - occasionally throwing a sheet of 4x5 in it, or finding a roll of appropriate film on ebay and sometimes actually getting images.
It would be nice to keep it "whole."
I've toyed with the idea of taking the strap to a cobbler and having it sewn onto a new, slightly wider, strap. That way it'd have a suitable strap while keeping the nostalgia.
Oh, and if you want the look of rivets, you can probably find a cheap tool online. Place the rivet in the die, place a shaft on the other side, and strike it with a hammer.