I'm doing something similar and was having a hard time.
After a lot of tweaking and some forum posts, I came to this method, which won't work 100% of the times but should give you a decent result.
- Download Zv parent master.
-Select the axe, then one of the hands, let's the say the right hand, and use the Zv constraint;
-Create an ik handle from the shoulder to the wrist of the other arm(left).
-In the attribute editor, set the ik solver to hiksolver, otherwise your elbow will probably be upside down.
-Parent constrain the ik handle to the axe.
-Orient constrain the left hand to the axe.

It will take some tweaking, but it is a good starting point.

Beautiful idea, I will give it a go. Thanks!

Thanks again for the input and sorry it took me so long to reply.

I tried what you suggested but did not have success. Maybe I need clarification on your directions. When you said to "Orient constrain the left hand to the axe" did you mean constrain the left hand skeleton to the axe? That's what I tried. I guess that's the only way to do it since you can't constrain the HIK effectors.

The left arm did not follow the axe (golf club in this case). The only result was that the skin of the left hand did change orientation, but the hand skeleton did not.

I think I'm screwed on this one!

I did just have some success. I changed the IK solver for the IK handle to ikSCsolver and the hand did follow along. However, everything downstream of the hand (all the finger bones) stay put while the hand, wrist and upper arm follow along.

I may try to add IK handles between the hand and each of the 5 fingers and parent them to the "axe" as well to see if that will allow them to follow along as well.