Does the wall appear to be solid or is it the common 1/10" and a hollow stud? If it is solid wood stud, any of the fill and reinstall may work. If it is hollow, use a jack rivet with a same size machine screw as the old wood screw, ie; #8 wood or sheet metal, use a 8 - 32 SAE machine screw.
Another trick that is better than toothpicks, is to sharpen a 5/16 birch dowl in a pencil sharpener, but a drill of the same taper and drill out the hole to a good fit, glue in hole and cut off the dowl drill a pilot hole and pilot drill for screw.
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