That's not a thermal reactor. It's the main cat. The one upstream is a pre-cat. The line is used to feed air into the cat for the catalytic reactions. You're going to have to decide whether to maintain the catalytic converter system or not. Do you have a functioning ACV and air pump? If not, then the cat's doing no good anyway.

Didn't get a real good look at the exhaust manifold, but it appears to be a normal '84-85 manifold. It's a big clunky cast iron thing - but not as big/clunky as a thermal reactor.

You can ditch the cats (main + 2 precats) and keep the iron manifold - should sound okay. If you replace the manifold with headers, you need to plan out the exhaust system a little so it doesn't sound nasty.

My own experience was that headers + cat (aftermarket) + stock muffler sounded kind of nasty. Went back to the iron manifold and sounded good (didn't make much difference in power due to my exhaust pipes being too small anyway).