Use a razor knife and a strait edge.
- Mount the strait edge to your popsickle stick so that it creates a hard edge right diwn the center. You can simply tape it to a metal ruler.
- Now set the razor knife on the stick and pull it lengthwise down the stick, maintaining a strait line, by keeping it tight to the ruller. You don't need to press hard. Just push it down enough to score the surface.
- Go back over the scored line a few times, lightly lressing the razor knife (scalpel, or exacto knife). Eventually it will work it's way through the wood in a very strait, smooth, and controlled manner.