The joystick software requires me to run the executable for the game in order for the joystick to work. but i can't run the executable outside of gog galaxy so the joystick does not recognize the game. Is there a way to run this game outside of the client?

Do you know for a fact that's why the joystick doesn't work? Or are you assuming Galaxy is the reason it doesn't work. Because I can't think of a reason why Galaxy would have that effect.

Anyway, if you want to avoid Galaxy, just download the offline installer for Gauntlet Slayer Edition and play it that way.