You could try to use Proton GE, which you just download, unpack and execute the proton executable in it. There are a few variables to set, but no administrator rights is needed. I wrote a little script years ago, which got a bit semi-viral (if we can call it that, but to me it was xD): proton script You need to read and adapt the parts, but at least you can see how this works. There is also a fork, who made an advanced version of it. I have no idea if these scripts work without Steam. But that is left as an exercise to the reader.
BTW its not really recommended to play non Steam games or apps with proton (because it could messup something on your Steam installation, but that is probably irrelevant on the library PC), but it worked for me for regular Windows applications. I did not need to install WINE for that and just used my Proton from Steam back then. Today I have no need for it anymore and don’t know how well this works.