I would certainly pass on the adhesive remover. You will get rid of the glue but likely do more damage to the rest of the wood. Give #7 a try on the wood, it should remove most everything but swirl marks/scratches. A coat of #26 should protect. The Meguiar's #9 Swirl Remover should take care of swirl/scratches. If you can't find (and still need) the #9 let me know and we may be able to help.

Lee