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The collector will have to be welded to the exit on the headers or you could use band clamps as stated above.
The best way is still to have the muffler shop weld the pieces together for your set-up, this will eliminate any leaks and will keep solid.
The collectors will enable you to be able to remove the exhaust after the headers if you need too!
It should actually be an inexpensive job for the shop to weld. Go to the shop and talk to the tech/welder and get his thoughts and then see what it will cost. If you do it this way instead of just taking it in and saying here they will know what expect you and will tkae care of you better. Just show some interest in them and they will return the interest in your Vette!
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.