An alternative to the rubber band is tulle, the stuff that bridal veils are made of. That and super glue gel are the staples of my fragging equipment.
As for cutting, anything sharp will do. A razor, pair of sharp scissors or even a sharp knife will do the trick. Ideally, you want a nice clean cut. Depending on the size of the piece, you may need something larger than a razor blade. (I had to use a bread knife for a massive toadstool once.) I generally use a pair of suture scissors for small things; a #4 scalpel blade is about right for tough, woody leathers.
Have fun - it not nearly as bad as you think it's going to be.
Danielle