I've been doing it exactly that way for several decades too. It does work. One exception: I usually leave about 1/4 to 1/2 inch of sting sticking out of the tuner when I cut it off. I've seen the string get sucked back into the tuner and come undone when I stretch it so now I leave some length so that it doesn't come back out of the tuner.

This is how to do it kids.