Thanks Dave and everyone else who responded. I've done this now: the
drilling went OK, and if there was any breakout under the panel it must at
least have been contained with nowhere to go: there's no sign of any loose
chips or other damage either inside or out, and the holes weren't impeded in
any way.

The hardest part of the job was driving home the fixing bolts - Multi-Mondi
hex heads from Screwfix. I had to use a small socket-and-ratchet tool and
the last few turns needed quite an effort. Indeed, the last few turns on
the first bolt proved impossible until I realised that I hadn't drilled the
hole deep enough...

Bert