At the very least, it could be manageable through a Steam controller profile. Its possible to play mouse-only, and there are assignable hotkeys that could facilitate better button mapping.

I'll try to remember to check how well it plays with a controller next time I'm on.

Its a very clear sheeme I also think, it should work though steam without a lot of hassle

Have stand corrected, there a selections and ui elements that probably wont work without some mouse surport (be it though controller analog stick) as shortcuts/keyboard input dont exist for them.