After ruining many a box tops I discovered a magic potion to do the job. Dawn Platinum dish liquid. After "thumb nail" removal of as much of the surgeon general's warning, put a few drops onto a microfiber cloth and rub away.. worked like a charm on a lacquered Camacho box .Have not tried it on a paper box yet.
Dawn is pretty much the Universal Solvent sought by alchemists for hundreds of years. it is also a good shampoo for a nasty under the car day.
there are 2 products that remove glue from anything: Goo Gone and Goof Off. I don't have enough ratbag cigar boxes to experiment on the effects on the finish and wood.
A hair dryer or heat gun on low is a good start for removing labels.
WD-40 followed by isopropyl alcohol to remove the WD-40 works great on some adhesives.