Quick Update:
Silly me!
All I think I have to do is cut horizontal slits in the outer pipe coming off the muffler.
Then the clamps will be able to squash it down and make a good mechanical connection between muffler and exhaust system.
This should make the muffler solid without welding, and it means I'll be able to easily remove it later when I want to replace the older pipe and Catalytic Converter.
I hope this helps others with similar dilemmas due to inexperience.