I really don't think that most of us who vapes is really inhaling enough cotton to present a health risk. There may be particles felt while vaping, however this is likely the buildup on the coil.
Everyone has their own method of cleaning these, I'm going to state mine. What I do when the flavor starts to get scorched, is to remove the coil from the tank. I have an exrta T3S base, for the purpose of testing rebuilt coils, to ensure that I'm between 2.0-2.2 ohms. This, I also use to burn off coils as they get crusty, that is, if they're not blown.
Remove the coil from the tank & then the chimney & gasket. The coil will still be attached to the base. I have an ego style mod, what I do then is, while the coil is still wet from juice, is press the power button on the mod for a couple of seconds at a time, smoke will begin to rise. Don't hold it too long. Do it in 2-3 second bursts about a dozen times, the smoke will begin to disappear & you'll begin to see the red glow. That's what you want to see, the crud is being burned off. Blow on it between this, this helps to get rid of loose particles.
Once it's good & fairly glowing all across, it's much cleaner than before. Place a couple of drops of whatever juice you're using (the same flavor) onto the wick & replace the chimney & gasket. Allow it to sit for a few minutes, refill the tank, replace the coil & let it sit for a few minutes to absorb. The first few draws may taste a little burnt, but that will go away & you're good to go until the next time.
This also extends the life of your coils. I used to rinse then with hot water, allow to dry then burn them off, however many times the coil would burn out, so now I do it as described above. This saves one from buying or rebuilding coils as often.
As for the cotton when I rebuild, I also use braided silica (ekowool) of the 2mm thickness & 32 guage genuine TemCO Kanther wire. It's important to use a torch lighter to burn both off before use (not too much on the silica), I make sure that the Kanther wire is burned until it's glowing, across the whole piece that's being used. Helps to handle the wire better, plus burns the oil off of it, which is likely far worse to breathe than anything else.
I really don't believe that the cotton alone will harm someone, unless it's the cheapest stuff that can be found. You get what you pay for in general, which is why I insist on Genuine Ekowool based silica.
Personally I believe that this *risk* of the cotton is overblown & chances are there's far worse things that many of us breathes daily.
Cat