It depends on the type of finish that is on the wood. Newer finishes are "catalyzed", meaning that they are a two part finish that hardens through chemical reaction. Older finishes are typically varnish or laquer and they harden by the evaporation of solvents. Once you add solvents back to the older finishes, they disolve again. If it's a newer type finish, you can use nail polish remover. The newer finishes are resistant to chemicals. It turns out that it doesn't really matter if it's new or old finish since you'll need to remove the nail polish anyway. If it takes the finish off, sand it down, get some new stain to match then spray on some varnish, laquer or polyurethane to match the old finish. If you can't match the finish, you may need to sand down the whole piece and refinish it.