The thickness of the shaft is no problem. I attach an exel-sheet, where you
can see this.

The difference in cross-square between a 0.5cm shaft and a 4.5cm shaft is

Pelton Wheel: Figure 135

Below you will find a Pelton Wheel article that was translated by Martin Boll. The original text is italicized.

[1] (The young machinery constructor)

[2] (A Introduction into the elements of maschnery-construction and instruction
for making small models)

[3] "Adams Machinery-Book for Boys"Der junge Maschinenbauer (The young machinery constructor) Eine Einführung in die Elemente des Maschinenbaus und Anleitung zur Herstellung kleiner Modelle (A Introduction into the elements of maschnery-construction and instruction for making smal
(Copyright 1909 By Harper & Brothers)

[4] There, where a relative small amount of water, but a stronger
pressure is available, we use as well a sort of undershot water-wheel, by
using the high water-pressure with very high speed to bound against the
paddles of the wheel.
"