For low voltage, less than 50VDC, as said cut groves in the foam, and run the wires. You can then run a small bead of expanding foam insulation to fill the grove and hold the wire in place. Trim off the foam that expands above the surface of the foam sheet. For a bit more safety, run the (+) and (-) wires in different groves separated by an inch or so. That way a errant nail or screw will only be able to easily hit one of them. For the studs you will only need small holes just big enough to pass the wires. Drill them before assembling your wall. Mark the stud so you can see where the holes are when the foam is in place.
Another idea, use Corrugated Loom (example:
http://www.waytekwire.com/products/1469/Corrugated-Loom/) for running your wires in. Available as small as 1/4" inside diameter.
There is also smaller sizes of Liquid Tight Conduit. (
http://www.waytekwire.com/products/1494/Tubing---Conduit/&Type=Liquid-Tight-Conduit) 3/8" is the smallest size.
Another option would be to take large ID diameter brake line or some other sort of metal tubing and use it as conduit. Flange the ends so they don't cafe the wires going in and out of the tube. Metal tubing will provide some protection against putting a nail of screw through the wires. If you use metal tubes, ground them. That way the circuit blows if a nail punches through the tubing and punctures a hot wire. Conduit will usually deflect a nail, but... that is only usually. Air driven nails will punch through metal conduit.
Waytek Wire isn't the cheapest place, but they have the stuff, and other vehicle electrical parts. They are more setup for the vehicle modification business rather than end consumers.