Most people don't consider it a problem unless they're trigger sticks.
I found this teardown of Ultimarc's Minigrip joystick.
https://www.flickr.com/photos/flightgeek/sets/72157632729561908/with/8458376189/It looks like the pivot is keyed. I don't see where the shaft is keyed, but it must be.
I don't see a way to do this without both those parts being keyed.
Both joysticks look to be based on a Sanwa JLW.
Maybe parts are interchangeable or could be made to work...
Email Ultimarc and ask. That is if you're willing to buy two more joysticks for the sake of having them not spin.
EDIT: looking at those pics again it looks like instead of being notched out, the stop made into the joystick shaft is flat on two sides instead of being round.
It looks like both that and the pivot would drop down into a hole with a corresponding shape.