I would hazard that you will need a DC fan for proportional control.
If I recall, the speed controls in overhead fans (with 4-foot sweep diameter, consist of switched AC motor capacitors in series with the motor. I don't recall if I wrote the details down, but this was how the Hunter fan in one room in my house works. There are likely some patents on such. There are lots of circuits on the web. The underlying motor has two windings, and is not shaded pole.
I suppose that for a shaded-pole induction motor in fan duty, a small variac would work, but would be a bit clumsy Maybe a tapped transformer.
Joe Gwinn