I don't think Rem Oil is intended for wood, either... and it does, I think, contain solvents as well as oil, and those could damage a wood finish -- especially a pink one...
(Sorry, couldn't resist.)
Clean the stock with mineral spirits to remove oil residue and dirt, and see what it looks like when dry. If it's still dull, give it a coat of paste wax. If that doesn't work, remove the wax with mineral spirits and give the manufacturer a call to ask what the finish is (it's probably some sort of lacquer, which oils will
not improve), and what product they recommend to "freshen it up." Not every "rejuvenator," etc., is compatible with every finish. But ya can't hurt it with wax.