Don't do the toothpick route. That's the lazy way of doing it. If you want to do it decent, use wood filler and fill that hole. Use something like liquid nails or Elmer's wood filler (sold at home depot). Fill the hole and pack it in as its drying, let it sit for a couple of days and then screw strap button in. I had a problem with my stock schaller strap buttons on one of my strats (the screw was loose) and once I did that, the problem went away.
Jimmy, as much as the filler does a good job in most wood working situations, It doesn't work well for a screw that will have any torsional (side by side) forces applied to it.
It doesn't work for a couple of reasons.
First- the filler continues to shrink for months after application......this alone will cause the screw to wiggle in the hole.
Second- When dry, filler is brittle. it will crack and chip INSIDE the hole.....this will be exaggerated when the screw above starts to wiggle.
Third....It is nearly impossible to fill the hole completely. There will be a pocket of air inside the cavity because of the pressure created while trying to push it in........ the air gap will cause more weakness.
The toothpick method is the correct way to repair this problem for a few reasons.
First... any glued joint between two pieces of wood is inherently stronger than the wood was originally.
Second- the toothpicks will swell when whetted with the glue. this and the glue will fill the hole completely.... when the screw is inserted (with the glue still wet) it will fill the void completely.........no air gaps.
Third- the toothpick method takes only minutes, not days, to complete.