I have been doing this for years now. I normally have a piece of plastic/saran wrap at my nail supplies stash to use when I need to remove my nail polish. After wetting the cotton with remover, I cover the cotton with the plastic wrap and put it over my nails when I am removing my nail polish, so my skin would not be in direct contact with the nail polish remover.
Nail polish remover can be very drying especially the ones containing acetone. So the plastic would be the protective barrier for my skin from the remover, since sometimes it can take a while to clean the nails. It also protect the nail polish on the fingers of the other hand if I do not want to remove polishes on both hands on the same day, which is most of the time! The plastic wrap can also act as a moisture barrier so the cotton stays wet for a little longer before requiring more remover.