Cotton has a fairly distinctive taste -- chew on some [clean] bluejeans, you'll see.
As for skin oils... I dunno. I've never had an issue, but I typically do keep my hands quite clean, because anything greasy or tacky on my hands drives me completely batshit -- I just put some lotion on my hands, because I just did the dishes and my hands were feeling really dry, and now I just can't wait till the lotion absorbs so I don't feel it anymore.
I never use lotion with any oils or perfumes, due to eczema, so it will absorb PDQ... meantime, it drives me crazy, feeling it.
If you feel something on your hands that isn't supposed to be there, then yeah, definitely wash up before handling the wick! A good way to tell if your hands are clean... look at your nails! If you can see ANYTHING under them... those hands aren't clean. And when you build a coil, it's a good idea to flame it before you twist it, then pulse it 5-6 times after you get it mounted, and then rinse; that will remove anything foreign/objectionable on the wire (machine oil or anything else, including the oils on your skin).
Andria