I had planned on a keybind option for the exact reasons you presented, but just never got around to it. Sorry about that! If I ever do get to reworking this game, it'll definitely be an option.
I'll take a look into it, but I think the way Clickteam Fusion handles controllers is they're either on or off, and by that I mean I include the controller support or I don't. I don't think the controller extensions for Clickteam allow me to turn off detection. Obviously keybinds are an option, so that would be fine for the future, but outside of that, I think if I disable controller detection, I disable controllers in general unless outside programs were used to enable them again in a roundabout way, unless I'm misunderstanding what you're saying.