Not exactly sure what you're asking, but welding in a replacement catalytic converter is a cost-effective way regain proper function-- I have had Magnaflow cats welded in to good effect for a fraction of the cost of bolt-in piece.

I am surprised to hear that a dealer offered to weld anything-- they usually push factory parts exclusively. That said, I would stay away from dealers (except to buy a factory replacement exhaust, which is of unparalleled quality). I think you will get better, cheaper service from mom & pop specialty exhaust shops.

Find a place that will put your car up on a lift, show you the problem and discuss what they want to do. Have you been told you need a cat, and if so, what were the reasons?