If you go with this method, you can use a microfiber towel.
I use this stuff to remove surface rust from parts on mild resto work (some seatbelts, cleanup jobs for customers who don't want to spend the cash to get it dipped, etc.)
It's also awesome to keep around the house. It removes grease stains from things like waffle irons, tea kettles, etc. Nothing else that I've tried removes carbon from exhaust tips like this stuff does with a microfiber towel and there is absolutely no risk of scratching or swirling.