Meat slicers scare me though they might make a good planer... though I think they would remove a greater thickness of soap.
When I was in high school, I worked at a pizza shop that had an ancient, very second-hand, dull meat slicer... the contraption was much older than I was. The blade would get stuck in the meat with oily smoke coming from the motor, and we had to push on the flat portion of the blade to get it spinning again. Of course this led to accidents...
One day my hand got caught on it, and it made the cleanest slice in probably 15 years over my pinky finger - from my knuckle, through my fingernail and around the top to other side - neatly exposing my bone. I was in shock, but must have made some noise since my coworker, Aparna, came over and looked at my finger. At just that moment, a spurt of blood hit her across the face and she fainted. Our delivery guy walked in to find a murderous looking scene, with me bent over a body on the floor getting blood over us both while hunks of ham fell around us. The delivery guy took me to get stitches, Aparna's husband took her home after throwing the machine in the dumpster, and the owner finally got us a curse-free slicer.
So, ummm, be careful!