EDIT: If it's a Bakelite socket or other brittle plastic, use dikes to split the remains of the shell into pieces and remove it. Just be mindful that you choose places where you can get a purchase with your diagonal cutters, and that if you slip when it gives way, the cutters can only hit areas that will be hidden by the new socket.
It will be, those sockets of that vintage are almost always made out of a thermoset, not a thermoplastic. It's only recently that people have been stupid enough to make them out of plastic that can melt. I think the existing fracture attests to it being a relatively brittle thermoset.
Rather than side cutters which, as you note, are one hell of a slip risk, try an automatic centre punch to break it up with. That way you can be sure that you're always directing force towards somewhere that will be covered by the replacement, in the unlikely event that it punches all the way through into the material underneath.
And with that note, as droogie Dim said "Bedways is bestways now." Nightie night.
That's a good idea... but if mansaxel has luck anything like mine, the random fracture from the punch will leave a nub under each rivet, both of which will be perfectly shaped to be as hard to remove without scarring the panel as possible.
One
might be able to crudely direct the fracture such that it bisects the rivet using dikes... I've done similar enough times successfully to know it is
possible. But not reliably, fer sherr.
EDIT: That reminds me... I've had good luck fixing Bakelite with CA, as long as the break is still clean before gluing. The shifter knob on grand-dad's F150 was one such repair... held up for years with him and over a decade of me driving it. Mans, it might be worth a try before you take on a battle to the death with the thing...
mnem
*heeds Hypnos' siren call*