I've yet to be able to remove a cotton wick. Sometimes it's more difficult than others though. I always take a pair of scissors and snip the cotton as close to the coil as possible and then pull it through. I even had to run it under water once and then the cotton came right out. Dried everything off - dry burned - re-wicked - reassembled - filled and was good to go.
It probably has a lot to do with the setup, but in my Kayfun Lite I use organic cotton and pull it through, assuming it's not burnt. Also in my RDA's, both using a standard microcoil at 1/16 or 5/64. My wicks are twisted from boiled organic cotton balls, and either about 3/8 to 1/2 inch I'd guess on each side of the coil for the KFun and RDA's vary.
I wonder if I'm wrapping mine too loose since I can pull the cotton out, although it takes a lil working back and fourth a bit sometimes to uncatch it if there's a bulge at the edge to get past.
Ohhhh I wonder if it's because I use 28 guage, or smaller coils. What kind of coils and wire size are you using? I'm wondering if I'm wrapping mine too lose, but now that I think about it I don't think I could get much more cotton in there and still pull it through.
Sorry for so many different questions but I've only been building a few months and trial and error with cotton fairly often only to return to "old faithful" because the new wick style I'll be testing either burns or doesn't breathe, etc.