Jeweller's cloth
The safe one is the one with nothing in it. Conservation specifies a cloth that works by the stiffness of its weave, not by an abrasive.
In detail
A close-woven cloth used to buff fingerprints and light dulling off uncoated metal. Conservation guidance clears it for exactly that — a jeweller's cloth may wipe or buff away fingerprints on uncoated gold, silver, copper alloys and highly polished steels where a piece has been inadvertently touched — and then adds the condition that decides which cloth to buy: SELECT CLOTHS THAT CONTAIN NO ABRASIVE, relying instead on the stiffness of the weave for their polishing effect. That rules out most of what is sold under the name. Many polishing cloths are impregnated with a fine abrasive or a chemical tarnish remover, and those are a polish in cloth form: they work by removing metal, which on a plated piece means removing a layer that cannot be replaced. So the distinction is not brand but construction. An untreated close-woven cloth removes what is ON the metal. An impregnated one removes some of the metal. Both feel identical in the hand, and only one is safe on gold plate, vermeil, silver plate or a gilded surface. Any clean soft cloth may be used to buff an object after handling; the specialist cloth is a refinement rather than a requirement.
Sources for this page
Sources
Museum Handbook Part I, Appendix O: Curatorial Care of Metal Objects
National Park Service, US Department of the Interior, 2002 · Reference work
Relied on for: That a jeweller's cloth may be used to wipe or buff away fingerprints on uncoated gold, silver, copper alloys and highly polished steels, that cloths should be selected that contain no abrasive and rely on the stiffness of the weave, and that any clean soft cloth may be used to buff an object after handling. (states this directly)