For stainless use MEK (Methel Ethel Ketone). Itwill completely remove all surface oils, residue, light stainsetc. Wear nitrile gloves and stay away from an ignition source. Well ventilated area. Static electricity will even set it off, so be careful. Sold at hardware stores."Lightly" use a soft scotchbrite pad. On stainless if it is a brown residue when wiping it is indeed oxidation which is a form of corrosion. Not sure how MEK will react ona nickel clad coating especially if it is a cheap thin coating. For Nickel I would stick to a less aggresive solvent like Naptha.

CAUTION: MEK and Naptha will eat plastic so remove metal parts from stock etc.!