That cotton looks OK. It's just rebranded facial pads sold for more money. Oh, and that CVS search outcome? Folks have used those pads successfully for wicks too. For real. Honest.
You do not have to clean or torch the wire. Torching the wire is only on some types of wire to help remove any "springiness" in it, not necessary here. When you build and mount the coil, after you make sure the resistance is OK, you're going to gently pulse the coil with current to make sure it heats up all evenly. That will burn off any residual stuff that might be on it. Wire from places like Temco (still can't believe that back order thing) or Master of Clouds arrives quite clean with no machine oil or anything.
Oh, and should you ever need to torch a wire (or certain fancy coil builds) in the future and don't have a blow torch handy, a Bic lighter works just fine by passing the wire through the flame. Just don't burn your thumb holding the button down.
