Plastic is tough

I was trying to build a contraption that would allow me to punch circles into the white plastic foil of my Ikea SAMTID lamp. Unfortunately the wood is too soft, the punch is too dull and the plastic too tough.

Epic failure.

I need something that can cut perfectly round holes that look good. Something like a compass with a cutter instead of the pencil tip.

Or a water jet, laser cutter... nobody has that in these parts.