Thus I conclude that all "small" shots cannot be utilizing the Rope Handle Technique and is thus not "swinging".
For shots that don't cock turn the Left Wrist, you're pushing or pulling a Primary Lever. The Left Arm and Clubshaft become unified. Therefore, there is no secondary Lever to propel through impact.
You can't push a Rope. A horse is pushing on the harness but is Pulling the cart.
When the force moving a weight is in front of the weight, it's called pulling (Swinging). If the force is behind the weight it's called pushing (Hitting).