Do you use that fireplace? Lowering the shelf brings a nice broad surface even closer to the fire and could possibly be a fire hazard of it's own. The manufacturer should be able to provide you with specific measurements and clearances that are acceptable. As far as the studs, they may be metal. A stud detector has a harder time recognizing thin metal studs. And finally, the wire.. 10 billion homes in this country have wire run for mantel clocks. They're run in all different manners but you should be ok running a romex or BX cable as long as you can keep it away from the fire box. (it may be kind of hard to route it where you want it) If you could run the wires down from the attic, it would be even better. Check the firecodes in your area.. You may have to use a firestop around any penetrations in the chimneyway. Lots to consider here.
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