Since I realized I overlooked a bunch of obvious ones I should have listed here’s a short list of a few more off my spreadsheet. Both things I’ve played and things I want to play.
Challenger for the famicom and Magic Wand both came to mind even though I’m pretty sure you play as an archaeologist and some sort of aged capsule toy collector in each, respectively. Both have immaculate cowboy vibes though:
This game looks so up my alley and I keep meaning to get to it. There’s also a samurai part in it right? Samurais and cowboys are equals on the coolness scale
I love this absurd game and its parry/dodge mechanics. Minigun enemies being able to erase your entire health bar at once sounds bad until you get the timing on the parry. Then you can return their entire bullet stream back into them and vaporize them. Plus it has the same costume/accessory system as Way of the Samurai, so you can dress yourself up as any character in the game, with a 400% larger hat, if you want. Universal model replacement ought to be a feature in every game by now.
2bears had a game years ago you might enjoy if you can find it then. Sixgun Samurai, it was a walking shoot game like ikari warriors except you only have six bullets and need to cut enemy bullets out of the air to refill your ammo. He never completed it but it was a decent couple stages