I was thinking along the same lines as CFT. When I go to work later, I will look for a HANGER BOLT (which is a machine screw on one end and a wood screw on the other) in 1/8" size to match the biggest collet I have for my Dremel. I also have lots of wine bottle corks and hadn't really considered turning them down till I read your post. I will chuck the machine screw end in the Dremel and use the wood screw side to mount the cork.

I'll let you know how it turns (get it -- turns --haha) out.

Clint