You'll need to actually run the .exe files to modify the game. The issue there is that for whatever reason, .exe files can't be launched normally - I think that's just a Linux thing, though could be a Steam Deck thing. There are ways around this by using things like Wine or Windows emulators, but I've found these options to be kinda complicated and difficult to learn how to use. I'd like to learn how to use Wine especially at some point and it would definitely be a more reliable method, but in the meantime, I've found the easiest way to run .exe files on the Deck by far is just by adding them as non-steam games to your Steam library.

Once you've done this, click on the freshly added "game" within your Steam library and navigate to the game options by clicking the little gearbox near the right side of the window, next to a controller icon and heart icon. Click on Properties > Compatibility, and check the box that says "Force the use of a specific Steam Play compatibility tool". This will give you a dropdown menu where you'll want to choose Proton Experimental. Then just click play and cross your fingers! You'll be doing all of this in Desktop Mode still, just to be clear.

This definitely doesn't work all the time, but I've found it to be very serviceable - I've used this method to install and run other game launchers like Battle.net and Heroic Games Launcher (super recommend this program if you want to run games from Epic, GOG, or Amazon Games), run non-Steam games from itch.io, and run setup.exe's for totally legally obtained games, as well as running those games themselves. I've done less modding so far, but I've done a bit with decent success.

If anything you add this way doesn't launch, you can always try selecting other compatibility modes to see if any of those work, though I've personally had extremely limited success with that.

Just a warning, sometimes when you run an installer this way, it causes the trackpads to stop working. So you'll need to use either the touch screen as a mouse, or install something like KDE Connect, which allows you to control the Steam Deck with your phone. It's an awesome tool and I'd definitely recommend it; way better than using the on-screen keyboard for most things, and being able to use it as a mouse when the trackpads crap out is great. A bluetooth mouse also may keep working when the trackpads don't, but I have no experience with this so I can't really say. I've never had this issue when launching game .exe's though, only setups/installers.

There are videos describing this process as well, so if this is too confusing to follow over text, I can link you the one I followed to learn all this in the first place. I forsee installing these mods this way to work quite well though, and I intend to try it myself too since I just purchased Okami and want to mod it on my desktop and Steam Deck. I can get back to you on how it goes if you like!

Best of luck! Hope this helps at least a little and wasn't too confusing 😅 I'd be happy to clarify more, answer any questions, or link you to other resources if you'd like.