you do want them through the wall. with a hole cut in the back of the cabinet for access. in several of my cabinets, the bottom shelf slides out so i can reach what's in back. the older i get, the nicer that feature is. but it means that you cannot have stuff coming through the bottom shelf. that said, it should be possible to run the wires on top of the tile to the back of the cabinet. not optimal, but not impossible. and there are receptacles that can be mounted on the surface. up near the top wouldn't affect the storage area within the cabinet. if it's not too late, you probably want electrical outlets in back of cabinets where you might want to put anything electrical. it sure is nice to be able to pull a plug, rather than to have to go shut off the circuit breaker. OH, and it's nice you're honored by first class idiots. you wouldn't want third class idiots, now would you!