I can't tell, is that a galvanized pipe? Or just crud covered copper? I am of the Mike Holmes school of "do it right" the first time construction.
If it's copper, sweat the valve off, using a big pair of channel lock pliares to twist it off. Clean and braze a new valve on. No I wouldn't bother rebuilding the old valve after 50 years.
If not copper / easily removed, then you need to enter the wall, find good pipe or preferably a joint and repipe from there, then put a cover or re-drywall/paint, etc..
Sharkbite can work well, but only if the pipe is perfectly clean, no pitting. It's still a half assed repair.
Sorry, but do it right. You will be happier. Have fun!