Or, alternatively, have the bottom end of the walking stick screwed on to the overtone tube, remove it and you got an normal overtone flute. Use a female thread in the bottom of the overtone tube, and the walking stick tip with a male thread.
No doubt that would work, but it is more high-tech than I care to approach.
...would it not work to have a bottom (end) hole somewhere, and a stopper just below, so when you have the hole open it acts like the bottom open end of the tube, and when you have it closed you have a tube with just the mouth end open(?) You would need the bottom hole big enough I guess.
Well, no, unless your "mouth" tube was exactly halfway down the flute, and even then, it changes the entire character of the flute... The thing is, when you stop the end of an overtone flute you make it so the the harmonic must be a "closed" harmonic - with an even number of nodes (go easy on me, I know what I mean, but can't express it), but you can't do this if you are stopping finger holes, which simply extend the pipe-length. When you stop the the holes halfway/partway, instead of getting the note a semitone down, you would get the full length of the flute as its lowest note!