The 2nd video won’t play for me, but I think I get the idea.
Instead of using constraints to do this in HumanIK, I believe you actually want to make auxillary effectors “children” of other objects in the scene. Select the Aux Effector then the desired parent (the sword) and press P to change the hierarchy. Instead of controlling constraint weight, you then just animate the weight of the Aux effector(s). This is how Autodesk shows it being done for their middleware anyway…