Yes the strands in wall voltage power cords etc are likely to be too fat. Some stranded wire from low voltage DC hookup cables or out of mangled headphone cord is probably best. Anything that's more than a third the size of the hole is definitely too big, gotta get the pin in there too without bending it, something around a fifth seems about right, though you can get some real fine hairlike strands, they have the disadvantage of getting stuffed down into the socket, breaking or otherwise getting lost somewhere you least want them.
Edit: though if some thin hairlike stuff is all you can find, you might be better off tying the pin on the CPU itself, take a long strand of it and wind it in a figure 8 round those 2 pins on the CPU, remembering that it will be a mirror image of the socket, and pack it down on there good with tweezers and make sure the ends aren't gonna pop out and short to another pin.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.