Usually there is not enough 'meat' to weld. You can always give it a shot with the thought that you have to buy new if it fails.

Replacing is easy especially if you have a cutting torch. You can cut the pipe without cutting the pipe inside it.

I kept having the problem (like you) where the muffler is in good shape except that the pip that is spot welded to the Muffler broke loose and spun. Therfore everthing sagged.

I bought a new exhaust and before assembling, I welded the muffler pipes better then the factory did. When the muffler is new, you can do this easily. Sa o far so good. I also bought a too for expanding slightly crushed pipe. Not the kind you beat with a hammer but one that expands as you tighten a bolt. The brand and name escapes me but if you want it, I will look on the Pegboard tonight. That tool is great for reusing the Tailpie and getting the Clamp dimple out.
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'75 Jeep CJ5 345Hp ChevyPwr and two motorcycles: it wasn't Volvos safety , it was Longevity that sold me