I had this EXACT same problem with my Jazz a couple of weeks ago before the MOT,
Don't change the whole exhaust.. I wanted to change that part myself, but the bolts were so rusted that there would be no chance to get them off properly.
take a wirebrush clean it up to a metal, pinpoint the hole, and take the Holts Gun-gum paste and cover it all up generously. its about 2-3pounds depending on where you buy it online and it will fix your problem.
as a precaution do the same thing to both hangers, I knew only one was leaking for me, but I decided to clean other up as well and saw a small hole there as well- Just spread it all over generously after cleaning to metal and job done.