I think you would parent the swing to the figure's hip?

So far as the "crank" goes, if you parent the hand to the handle it should stay with the handle when the handle moves.  You might have to save the hand grasp to your Pose Library and then reapply the hand grasp pose if you change the figure's pose, but the hand should stay with the handle.

When I parent an prop/figure that is created for that particular figure IE: V3, I use the FIgures Menu and "Parent'.

If I'm parenting a prop/figure that was created for one figure, to another figure IE: hair for V3 and being used on A3, then I go to Geometry Menu and "Change Parent".

I wouldn't have a clue how to use the Hierarchy to parent anything.

"It is good to see ourselves as others see us. Try as we may, we are never
able to know ourselves fully as we are, especially the evil side of us.
This we can do only if we are not angry with our critics but will take in good
heart whatever they might have to say." - Ghandi