Well, as an update: it turns out that the weld didn't rust - it just broke. In cleaning it up I noticed almost no rust - just a broken weld. I wire brushed it and got the dremel out to clean it up and give a nice steel finish to JB Weld it back together. Two coats later and it purrrred like a charm. Unfortunately now three days later it broke. Apparently JB Weld is a little too brittle for the shaking/vibrating of a '97 Civic exhaust...at least in the winter. ANyway, now I have the un-enviable task of grinding/chipping it off so that I only have to pay for a new real weld, and not for the muffler guys to torch the JB weld off as well. Any suggestions for how to get the JB Weld off in the easiest way?

BTW - whoever suggested the sleeve or fitting to splice the muffler back together, that wouldnt' work for my case since the weld broke exactly right at the muffler so there's nothing attached to the muffler to slide a coupling over top of...just a hole. Thanks for the idea tho.