Use a cloth to get a better seal & protect your hands, but the exhaust gases shouldn't be that hot anyway (By contrast my old Rover's exhaust manifold got well above boiling within a couple of minutes from cold- so even if you've only just started the engine, be careful at the front end).
As to the corrosion- tap it gently with a screw driver, if it doesn't fall off, dont worry,
even if it does the metal exhaust repair bandages are pretty effective while you decide what to do- been running with one on the mid box of my 164 for just under a year
Alternatively, I did once run a SAAB 99 with a coke can pop-rivetted to the front box as a repair.
Don't remember if it made it sound any better
It lasted fine until I took it for an MOT & the inspector stuck a screw driver through it. (Naughty- MOT requirement is that the exhaust be gas tight, but test centre was also a tyre & exhaust place).
Also- make sure you get a few quotes.
Am thinking about a stainless exhaust for mine (might treat it out of the insurance money after it's repaired)
But quote for a (164 V6 cat back) stainless system was £380. mild steel was £150.
small difference, unless your going for the sports option.