Jason,
If I can get a word in, there are a couple of ways I might consider to attack the problem.
1) send it out to a sharpener..saw blades, scissors etc.
2) I have a small sander with a 1" x 42" belt and a 9" disk. I would use a 250 grit belt and approach it very carefully at the angle you think matches the one on the tool. Any grinding is going to be fairly slow, especially on a used belt. I use this approach to sharpen my hole punches, except that I will chuck them up in a 3/8" drill. Turn the sander on and the drill and it only takes a few seconds.
When the 250 grit belts get completely worn and won't hardly cut anything they become some of my best belts. I use them to burnish the edges on some of the thicker practice pieces I make. It will usually darken the leather, so don't do it on anything that you want to stay natural .
3) glue a piece of wet or dry sandpaper to a piece of glass and very carefully do it by hand.
Don't know if any of these methods will help you.