Comment by mitkebes

Just add the launcher to steam, and you can set the input profile for the game just fine.

Better yet if you use Heroic instead of the official Epic launcher, it will let you add the game directly to Steam.

This is basically how people use 3rd party games on the steam deck. You want them added to steam as 3rd party games for easy access in game mode, so you just add any non-steam games to steam. Heroic and other launchers make it pretty effortless, but you can do it manually as well.