jeweler here! though fair warning I know almost nothing about watches. any polishing cloth meant for precious metals is almost guaranteed to scratch a mineral or even sapphire crystal given enough time, but would probably do wonders for any tarnish that gathers on a silver bracelet. this is because most jewelry polishing cloths have red rouge imbued in the cloth. red rouge works well for polishing non ferrous precious metals, but would stain stainless steel (yeah, I know) or most crystals (especially acryllic and mineral, though also sapphire depending on the age of the crystal itself and the number of microscopic scrates in it.) they do, however, make cloths without polishing compound. I would recommend a selvyt premium polishing cloth, which tbh seems to be what you have in the picture. you can get them on riogrande.com. they don't have any polishing compound in them, and have an equivelent natural grit of more than 20000, so they wont scratch your crystal. these would also work well to repolish a bracelet by rubbing a bit of green stainless rouge on the cloth for stainless steel and red rouge for non ferrous precious metals. just dont mix the two, as a compound made for one metal rarely plays well with other metals. also, any cloth with a rouge on it is unsuitable for lapidary work (crystal polishing).