The PROPER method to clean an electrical contact (pair) *that is meant to be serviceable*, is by a process known as "burnishing". The tool is a flat strip of thin metal with a face surface texture of about 3600 grit. Short of having such an easily obtainable tool, the best and second and ONLY other proper method is the "paper" suggestion, but I would choose something a little stiffer than paper towel, also exhibiting far less fiber. So, I would use matchbook thickness or business card thickness media. A business card, in fact, is a good, if not excellent choice. Not an enameled version though. The paper is a refined wood fiber pulp media that has the perfect mild abrasion qualities required for the task. A true abrasive cloth is not proper, and is meant for other applications. If the contact faces have become pitted or damaged from an arcing/ current inrush event, you will likely not be able to get the original face shape back. If it is your lawn mower "points", you replace them, though I have made several keep on tickin'. Those WOULD require at least one of the contacts be abraded.
For normal every day use though, you should never have to worry about it, because any contact(pair) made from a proper media will be one of those we (science) knows to be of a low oxidation factor, or of one where it matters not. I believe, and only from _some_ experience, so not expert, that Platinum is most common in small scale applications, Gold is second, and most common due to modern electroplating and alloys of gold being able to be referred to as Gold, another is Silver, often used for RF where refined HV arcs would be encountered and oxidation layers are OK.
Use the paper. Non conductive AND high Volt per mil isolation? Use transformer paper. Top brand is "Nomex". Made by DuPont many decades ago, and barely matched (others exist). Something on the order of 1500 Volts per mil, IIRC, though I would recommend at least 5 or 10 mil media to acquire the stiffness to push as well as pull on it while clasped by the "contacts". 15 mil even better.
Have a nice day...