Cotton is cheap. Why would you want to reuse it?
IMO, there is a time to use cotton, and a time to use silica. I've found that cotton is a horrible wicking agent in some aspects. I have yet to find a good solution to using cotton in stardust atomizer. Most of what I use now, cotton is preferred, but not everyone prefers my type of atomizers. So, I keep a supply of Silica on hand to help others.
For those who do not have a supply of silica, they may want to clean the wick. Silica can last a long long time. I've used one piece of silica for half a year once, and I changed it just because I changed atomizers. I tried cotton in my Genesis style, but it didn't keep up with the wicking demand, and I was getting constant dry hits. Silica can be torched and cleaned that way and is very resilient.
IF you're using a pre-built wick like in a CE5, protank, vivi nova, etc, the best thing is to just rinse it out as much as you can. There's not much you can do. If you get some supplies, you can venture into rebuilding those, but once you take apart one of those coils, you cannot put them back together efficiently using the same materials (if at all). I do recommend rebuilding them when they get gunked up. It's easier than you think.