You can also use sewing thread held taut (either with your fingers or a saw frame). It's the cleanest method I've found (the friction heat melts the sawdust together, you just pull it off like flash after you've completed the cut), very flexible (I've used to use this trick to remove doors from car model body shells) and unlike razor saws, you can usually use both resulting pieces if you're careful because thread has virtually no kerf.
Barring that, try scribing with the back of an exacto blade. It may sound paradoxical, but being patient and going slow is the fastest way to get a good result. Good luck!