My Spacesailer 24 has a diesel with the prop immediately in front of the skeg mounted rudder. I have been sailing with the gearbox in neutral and the clutch disengaged.
Recently had the prop shaft refurbished, and the bottom rudder gudgeon was removed for the job. (Should have checked the play, but I was not there.) Top mount is a tight bush.
At a certain speed under sail- maybe 3+ knots, the tiller starts to vibrate fairly rapidly. Doesn't move, just feel the vibration in my hand.
My guess is it is the prop whirring effect and not a loose gudgeon.

Next time out I will lock the prop in gear, but any comments from those with similar experience?

Try putting the gear lever into gear with the engine turned off. That will stop the shaft from turning.

Sounds like it's shedding vortices off the skeg or rudder.