Yes it will. My thoughts are to suspend a small piece of tubing the length of the axle travel to the bottom of the frame. I would have a larger tube on it allowing it to slide as needed. The wire would be fastened to that. Pretty primitive but seems the simplest.
What about something like this: http://www.cableorganizer.com/gortr...-13-0&ef_id=Vg1CvAAAAa@BQw-h:20170215171715:s