Just sort of thinking out lout, no need to take it too seriously, but what about a very small PVC pipe running along the edge board?
Or better yet, if you have the plastic-sticky kind of edging, you could peel it up, run your wires, and stick that part back down. Might want to get more of your edging though as theres a chance you'll need to put down all new edging if it's old enough it's lost it's stickiness.
Anyways, like I said, thinking out loud on this one.