Neat idea. I've also used the cutting wax tubes for years. But I'm not as creative as you.

I just sort of brush the end of the stick against the teeth of the blade while running so that it kinda rakes off the end of the stick. That picks up the wax on the teeth, some of which then deposits at the leading edge of the cut. This produces an accumulation forming just ahead of the blade, and as it progresses, the wax is drug into the cut a bit at a time providing lubricated blade for the rest of the cut. On longer cuts, I repeat the process.