We're talking cocktail, not upright. The parts differ. We're gonna confuse the guy.
When in doubt, hit the manual's parts list!
Pac Man cocktail uses four #8-32 carriage bolts to hold the joystick, and four #6 x 1/4 "phil. trs. hd. scr."
I assume that means Phillips ?? Head Screw. (What does "TRS." mean?)
Galaga cocktail: Same thing, but the manual says 14 screws required. I think that's a typo and meant to say 4.