I can see how it seems this way, but these are both mistaken. Different tip shapes may result in tiny differences - not tip sizes.
pj
chgo
This is correct.
So much misinformation floating around here. Shaft/tip diameter will not effect spin. You can draw it out with a piece of paper pretty easy.
Tip curvature plays a small roll, but assuming a consistent tip curvature then shaft diameter will not matter until/unless you reach the edge of the tip, where the skinner shaft would hit the miscue limit earlier