Xander, thanks for the reply. I have already done everything in your post-
Tried both "point" and "parent" constrain, and tried creating the constraint with a starting weight of zero, but it acts exactly the same. It is still clearly influencing the arm/hand even though the weight is set to zero.
And yes the constraint is to a control object rather than directly to the ikHandle (this is a pretty standard rig).

Can you think of anything else I may have done wrong?