That's a solid looking truck.
Not too long ago I came home from work and my 65 C10 had had a massive blowout on one tire. It was just sitting in the carport. I had been under it many times wihout jackstands, but now I don't get under there without them in place and I would advise you to do the same. Don't trust the tires
I was under my '65 a few months ago and got to looking at the tires, and immediately went and got jack stands. My thinking was that I was done for if a tire decided to give out while I was under there. They're still holding air, but when I get under that truck, because the tires are old, I always put jackstands under before I begin work.