The general answer is yes but the shaft will need to be plugged & re-threaded.
There are different designs of a pilot that may come into play but the procedure is the same.
The Schon that you mentioned has a pilot system that is somewhat unique.
The capped bottom ring with incorporated pilot, the brass insert and the shaft wood
interlock to one another and support each other and the joint as a unit.
Removing the pilot & insert will remove that desirable condition.
It can still be done, I'm just informing you of what you will be losing in the process.
Basically it becomes like every other big pin shaft at that point.
I'm going to suggest a phenolic insert/plug.
That may give you some of your 'zing' back.
KJ