Beware of all the different ways people clean their reflective surfaces. They gladly report how their method works, because they have had success with it. Yet even here on this short thread, none have told you what that surface is. In fact you also did not specify the surface of your mirror. If it is a bare aluminum vs. aluminum overcoated with dielectric vs. just dielectric vs. silver uncoated, etc. etc. Yes you can get away with cleaning a hardened reflective surface with wipes, at least a few times, but at some point the odds will catch up. Unless you are in a clean room, wiping with anything could carry along an inadvertent sand grain, or the like. In any case, if you are following the advice from someone who has a hardened surface mirror and you don’t you’re likely be sorry.
The best method for all surfaces is basically the one that @andrea tasselli described. No contact with any wipes needed. He left out, if need be, spraying or pouring over with a solvent for any stuff resistent to water/detergent. Solvent meaning something like alcohol after which the water rinse, then copious dH2O rinses. The fault you made with particles following the cottom ball path likely was the result of the solvent (dH2O?) you used having dissolved any soluble materials in the cotton, which when deposited on the mirror and dried, leaving non-volatile residue where a tiny droplet was left behind. If you did not use distilled water, then the stuff was probably soluble salts in the regular water. His suggestion to remove the last distilled water from the surface with forced air is very important. Yes you would expect distilled water to dry without residue. Reasons such as, distilled water never being perfectly pure H2O, or the dH2O actually dissolved something on or near the cleaning area, only to redeposit it when droplets dry. Removing the droplets completely avoids that problem. I basically raise and support the primary on its side in a tub and do just about everything with a squirt bottle. No need to touch the surface with anything at all.
And yes, the flashlight, especially an LED flashlight, is a very tough test. So as others have said, you should not fret too much. Also, avoid cleaning too often. I have heard that professional observatories do not clean their large surfaces until the dust is thick enough to cause several percent of the light as lost to dust. Even up to and beyond 5%.