I'd say you'd have less work but more money in replacing the whole thing. How is the rest of your set-up? Do you have an OEM intake manifold?
For the cut and weld approach, you'd probably have to flare the header, and the exhaust pipe after sliding new flanges on. I couldn't do it, but sounds like you have the ability.
While you're at it, you might just as well clean up the headers and strip them with phospho-etch, then paint with exhaust paint. That way you'd get a little more life out of them, maybe?