My method:
1-Dab of white or yellow wood glue on bamboo skewer (though you don't need the glue at all, but it will be good if you think you will be taking things apart later and don't want to have the skewer fall out)
2-Put skewer into hole and snap skewer to side but don't break it free.
3-Start the screw into the hole a few turns.
4-Now break the skewer off and finish putting in the screw.
This eliminates the biggest problem, which is the skewer falling out of the hole or moving around. Once the screw is in a few turns things are pretty bound up and not going anywhere.