How would one go about cleaning this tail pipe?

Yes Polishing soap will clean the metal. It will protect it. And in some cases it will help add some shine. I have used it on a lot of exhausts and even a set of wheels which were "brushed." And it did nothing to change the way it looks. As long as you're gentle enough you won't change the way it looks. It's when you start scrubbing vigorously that you may end up causing some change in appearance..

0000 steel wool is easy enough to work with. The only way you will cause any damage on exhaust would be if you use force or go straight up and down with the tips shown on the Cayman..