Wood screws are always a weak point in guitar building. If they're in a place where they only have to self tap once and only get removed/re-attached a time or two, they're ok. But if they're in a spot where they get screwed in and out often, the wood they're screwed into is soft, or if the first time they were installed they stripped, they're a real pain.
There's another permanent solution that's repeatable without fear of stripping. It'll take a little extra work, but not so much as to make doing it too much trouble. Thread these little dudes into the wood, and replace the wood screws with a suitable size machine screw, and the problem is solved.
In various sizes they can be used for bolt on neck mounting, fixed bridge mounting, pickguard holes, and yes, even pickup mounting directly into the body wood. Sometimes you can get lucky and find a suitable size from a local Ace Hardware, or you can always order them from a place like McMaster Carr.