Medical clinics and hospitals use small adhesive removal swabs to remove the adhesive left behind from dressings, etc. My wife being a nurse, we often have several around, and I've found them wonderful for the type of problem you described. I don't know if pharmacies carry them or not -- they come in individually wrapped packages (similar to an alcohol swab) with "Adhesive remover" in red print on the packaging. They're great. Ask at the local Rite Aid, or perhaps you could snag some from a nearby clinic?? Alternatively, non-acetone based fingernail polish remover will probably. Whatever you use, try it first on a scrap piece of wood to ensure that it won't stain, bleach, or otherwise discolor the wood (especially with the fingernail polish remover).

Nick