I design products and my implementation of physics is peer reviewed by The Analysis Department who have Doctorate's Degrees in physics to assure that my designs have sufficient Margins of Safety.
With that said to the first part.
The bending will be extremely small as you said and was my hyperbolic point. I thought that example my would be obvious to most readers except for pedants..
I wanted to express that a large wooden dowel is more rigid than a normal or a low deflection shaft and would produce a more visible squirt.
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0014" deflection if it is a 1.13" diameter broomstick...negligible.
Perhaps I should have said an alumina dowel with a radius on the striking tip.
Be well