On Thu, 18 Sep 2014 14:51:38 -0700, Jim Thompson
wrote:

I have some blank wall outlet cover plates, claiming to be "nylon".

Do you think I could punch a hole thru one of these with a chassis
punch, or is it likely to shatter?

...Jim Thompson
If you need a round hole - a wood boring bit with "tangs" on the
periphery so the outside is engaged as well as the center called "brad
point bits," or spade bits like Irwin "speed bore" style.

What I've found to be exceptional at cutting all plastics is the
"multi tool" which uses a small blade and reciprocal oscillations to
cut. (like those things doctors use to remove casts - but with real
cutting edges instead of a wavy edge)