Can’t answer your question, though of course Perspex can be cut. Coffee shop laoban here in Tainan who was in to DIY (made his own coffee roasters. etc) was going to make a screen for my RZR using a bench bandsaw, but I wasn’t back for a while and then the shop closed. DIY you’d need a fine-tooth blade in a jig or fretsaw, and you’d need to practice a lot, since screwing up a new screen would be annoying.
I wonder if it’d be usable left intact, with the light going through the screen? Unfortunate that the screen is smoked. Might be OK, or it might chuck light back in your face, but if you’ve already got the parts you may as well try it.
mask out the area with masking (painters tape) and take to it with a dremel… make the hole a little smaller than you need (as your cut will not likely be super-smooth) and take the rest off with some sandpaper / smooth it at the same time…
Smooth the edge with wet and dry paper (fine grade) used wet, with detergent and water. Use the paper with a sanding pad or block, and wash it fairly often, else it’ll likely clog.