Looks like an interesting 18th century gun.
I think that would be a really bad idea to weld and shoot. The barrel failed once, no reason to assume that it would not fail again, either at the repair or elsewhere. Even if it weren't split, what is the condition of the barrel? .
It might be possible to rework the barrel to bring the edges together, weld the seam for a cosmetic repair. I have "stretched" cut barrels to restore their length with o/a, and the joint was next to invisible after finishing.
If welded, dressed and straightened, it might be possible to ream out the barrel and install a liner. If this were done, it just might be OK to shoot it.
If the rest of the gun is worth the effort, making a replacement barrel would be the safest option for shooting it.