Roto-zip might be you answer

Roto-zip could work well like the other poster said. If you don't have access to one, you can also use the abrasive sanding bits for the dremel, you may chew through a couple, but they work in a pinch.

Go get a diamond hole bit and use a coke bottle full of water with a hole poked in the top to cool and lube it. Use a drill instead of a dremel. You will likely chip the fiberglass (I'm assuming that's what you think is plastic) if you try with a rotozip bit.