Matchsticks DO work. They have to be inserted in threes, to spread the 'squashing,' effect evenly around the screw shank. This works best up to No8's, therefter, you need more packing than matches provide.
Skewers are harder wood (or, at least the ones I have are) and, depending on hole diameter, may even have to be centrally pierced...a complete, frustrating, but necessary, faff...
The 'old timers'I worked with 40 years ago would whittle a plug to (just!!) jam-fit, very rapidly, with their ever-present penknife and then re-drill , gently, for the replaced screw. Slower, more methodical, but worked, with no dramas.....
Unless, of course, you didn't whittle to JUST over size and your over-size dowel acted as a wedge...like my first two did...the 'oul' fella' - foreman - just grinned, said "slow down, treat it like a wuman, approach with care and ease the fit"....
He was right.
Sam