I know how orient constraint works for the most part but what I am trying to do is I have the joints of a hand and I have a cone that I want to use to orient constrain the hand to, so the hand follows the orientation of the cone. I have my hand skinned and in it's bind pose. I also have the cone in the position I want. Basically the cone lies in the palm of the hand, where objects would be held. The only problem is that when I orient constrain the joint to the cone the joint rotates to match the cone (good) and it is no longer in the correct pose (bad).

What I want is for the joint to already be orientated to the cone before I apply the constraint so nothing moves out of place. How do I go about changing the local rotation of the joint to a precise value, and how do I find out what that value should be? I can eyeball it but it is not exact, I would like to learn how to make it exact. Oh, also I froze the transforms of the cone so it's axis is in the default position. The image below might help explain this a bit. Thanks a lot.