Three things I'd try:
Bore a hole in a wood scrap, put the stick in and wedge it, and fill with paraffin wax. Then,
with a heavy workbench vise, you can hold it still for a swipe or two with a sharp plane.
Low-angle (block) plane would be suitable, maybe a final pass or three with a card scraper.
Hole, wedge, wax again, only this time make a crosscut pass with a steel plywood blade in
a table saw.
Hole, wedge, wax again, only this time make a light pass with a straight carbide router bit.
Planing a loose knot is a close approximation to the task you have ahead of
you; making it a NOT-loose knot would be a high priority.