The orthodox method to do that is to use soft cotton or cotton cloth dabbed in cooking oil or coconut oil- very lightly as necessary. Rub gently on the spot/place. Clean off excess oil with dry, but soft, cotton cloth. Alternative to cotton cloth is the plain soft tissue (Kleenex, Puffs, etc). This method also works very well on CD covers where they put some sold/sale stickers that leave behind the glue marks. I had accidentally purchased a wrong L-bracket (Really Right Stuff) for my camera for $50. The low price was because of the adhesive on the bracket from a sticker. I eventually cleaned up the adhesive (2 mins) and sold it again for $80 + shipping :-)
BTW, oil is good for wood!!