Fill the hole with a piece of doweling with a tiny bit of glue on the end and then re-drill using a bit that is much smaller than the screw. You may want to mark the drill shaft for depth with a little tape to prevent going too deep.

I have a healthy selection of guitar -ish bits of doweling form tooth picks to wooden kebab sticks for just such repairs (i.e. filling holes left from old swapped out tuners) !