If you want to try the "eco" or "green" way to clean copper, brass, silver, etc. try smearing ketchup (yes, that tomatoe stuff in a bottle) on it, let set for 5-10 minutes, then take a heavy cloth (old towels work great) and start rubbing. It cleans quite well. If that doesn't do it, Brasso. It'll will clean most metals. I'm not familar with the Noxon.
I just lost 4 of my 6 pieces of antique solid brass hardware on an antique cupboard. Will cost up to $75.00 each to replace them. I've learned the hard way