No, I would not weld it. There are many transmission parts places on the net. They usually re-line bands. Yours has seen its day.
for one of the transmission parts places. ID your transmission, first. If you don't know how, CLICK HERE
. Then, call them (or ask a transmission shop in your town, where you can buy parts). Most of the local places are happy to help anyone with a classic car. Some of the old timers may have a band laying around.
If you keep your trans fluid level up, bands usually last over 100k miles because the fluid bath spreads the heat. - Dave