This discussion might be of helpMy experience is that you need the channel or else the adhesive comes off with the humidity and variations in temperature... https://www.houzz.com/discussions/how-is-led-light-fixed-to-the-steps-and-handrail-dsvw-vd~200847

Brilliance makes a good strip light or rigid bar light you could affix to the bottom edge of a tread. I have never been a real big fan of this type of lighting as I prefer a fixture mounted higher up on a wall to illuminate a larger area of the step more evenly and do away the with "hot spot" on the stair riser. It's all personal preference though. http://www.brillianceled.com/AC-LED-Strip.html