I have a old bass amp with a 2-conductor cord & plug. Lately, I've been working in a basement studio & I've been getting shocks if I touch the microphone while I'm playing. Would changing to more modern 3-conductor power cable solve this problem? If so, how to I attach the third (ground) wire to the amp & how do I decide which wire goes to the wider pin?

When I was a kid, I use to get shock from Pinball machines, and would simply remove plug from outlet an plug in reversed.
3 Conductor would be good, be sure hot and neutral are correct, If it doesn't shock you the other direction then remember and now you know which needs to be neutral and which needs to be hot. Be Careful, Good Luck.