I've worked with power tools for 30 years, and a slight imbalance in the drill can cause your rod to wobble into pieces quickly.
Cork will sand down easily, and I'd be more comfortable wrapping some 80 grit around the cork, squuezing with one hand and turning the rod with the other. You can even use a file to remove a good bit of material before switching to sandpaper. Tape the reel seat well to protect it from the sandpaper.
Auntrout: An extra bushing of tape wouldn't hurt. The glue is applied to blank, so your extra bushing won't prevent glue from reaching the cork, and it's small enough that it won't interfere with glue between cork and blank.