Chemical to remove nail polish but retain ink
It would depend mainly on the chemical composition of the ink (permanent marker? standard ballpoint?)

If it was signed with standard ballpoint, you have a problem, because the main film forming / thickening agent used for ballpoint pen ink is the same used in the majority of nail polishes - nitrocellulose. This means that a solvent that removes nail polish (ethyl acetate, for example) will also remove the ink.