FWIW:
a woodscrew's pretty much a wood screw functionally. Most pup screws are #6 or 8. Length can vary from bass to bass and preference string spacing but at minimum pup thickness at the tower + pad + about 3/16" into the bass. You want a rounded phillips head ideally that drops through the tower hole and is snug but no drag which would cut into the tower.
Home depot or Ace hardware may have a screw that will work but getting the length and rounded head may be a problem cause it doesn't really suit any home application at that size. GC or the like may have pup screws, I've never asked.