There are actually a couple runs of relatively modern grounded, albeit still old and crappy, grounded wire in my basement, including one powering my shed that ran right next to this outlet, and its shitty old ungrounded black cloth cable. I hijacked that and repurposed it for this outlet.

So, no shed power, but this first job gave me the confidence and motivation to tackle the rest of the house now.

Had my friend on the other side of the wall hold the terminal

use a ground screw or a grounding clip from the receptacle to the body of the metal box.

but likely a moot point because the receptacle itself has no grounding lug.

Just handle the old wire carefully. Baby it. Better still, replace it with something new. New stuff should last you 100 years. The old stuff, well, you can see how well that ages. Synthetic rubber & plastic technology was in a very primitive state before the 1970’s. That’s what the wires are insulated with- a form of synthetic rubber or an insulating type of plastic. Modern insulation (mid 70’s and later) are all forms of durable plastic that should last a long long time.

exception: electric cords and extension cords pre-1990’s… still a lot of older insulation materials that were prone to degradation with age/sunlight/ozone/heat but it wasn’t getting put into a wall in a house that could catch fire so no biggie… Any issue or defect would become apparent very quickly to anyone nearby.