Here you go buddy.
Pic 1 - You can see the shaft, no threads.
Pic 2 - the base of the shifter knob that I have. It is also unthreaded and is designed to be a press fit with some set screws,
Pic 3 - the new shifter knob in place. The perfect type for a sequential shifter.
I had to fashion a bushing to go over the shifter shaft that would be wide enough for the knob to slid over and have no play.
Your idea of wrapping the shifter shaft with tape might work out quite well. Just be sure to use wide electrical tape, and wrap it around the shaft clockwise, until there is enough tape there so you can twist the new knob into place. It might work out.
Hope this helps.