Have you ever used a pin vise before? It's a manually operated drill about the size of your finger and used for small and delicate work like jewelry or model building. You can probably find them in Jaycar, Hobbyco or on ebay for around $10.
With a small size bit, you can drill a pilot hole into the offending peg. It doesn't need to be all the way through.
Then, with a larger bit, drill into the same hole. You will feel a fair bit of resistance as the larger bit digs into the sides of the smaller hole. You can use this friction to grip the peg and pull it out.
edit: Actually, you could probably use a wood screw instead of a larger drill bit to pull the peg out of its hole.
Last edited by CBratron; 11th June 2015 at 07:48 PM.
Any figure that comes with swords demands wrist articulation.