Proton is certainly "cleaner" to use with Steam, but you don't have to use Steam to use proton. I'd recommend adding the executable to Steam as a non-Steam game for simplicity. Otherwise you can use Lutris or find a tutorial online to run that specific executable with proton outside of Steam

Yes, Proton is primarily a Steam thing, but it's free software and it's being actively ported to other launchers as umu (not by Valve). The project is very new and I'm not sure it perfectly matches Proton behavior yet, at least as far as game-specific tweaks are concerned.

Personally, for a non-Steam game I would just try to run it via Lutris. Lutris tries to automatically setup everything so you don't need to tinker with anything in the best case. It even automatically downloads the game installer and wine, and you can configure it to use the aforementioned umu instead of vanilla wine. In the ideal case, you get the game installed and running with minimal effort all from within the Lutris client. The problem is that the Lutris scripts are maintained by the project itself with recommended corrections from the community. So it's possible that a game could run with tinkering, but it hasn't been automated yet.