I'd warm the labels up with a hair dryer (NOT a heat gun), and the glue should soften enough to get them to peel. Then use Goo Gone to clean the residue.
Cleaned them all off last Sunday, and removed remaining goo with Wd-40.
I also cleaned and lubed all the drawer tracks, so the drawers work like new.
I pulled the wheels out of the casters to lube them, and was surprised to find they have replaceable bearings, like bicycle wheels. Ball bearings in little cages, and cones on each side with a spacer between. Cleaned and lubed them and re-assembled, and the wheels roll smooth as glass.