Stuff that thin can be scored with a matt knife and broken on the score. With care, even on a curved score. For curved shapes, make a template in thick cardboard and cut along that. If you need to do this more than once, soak the curved edge in a very thin cyanoacrylate glue, then file it to the final shape. That will resist scoring by the blade.

Today, I have a Dremel Scroll-saw with a fine plastic-blade. Makes life easy. I tend to cut a bit proud of the final shape and use a very fine sanding disc to finish. It gives a nice edge and no flash.

Peter Wieck
Melrose Park, PA