How to get a bone to rotate while still following a target?

I’m attempting to create an accurate (ish) skeleton (referenced off a rat atm)

Right now I can rotate the hand all around and the radius will follow in the correct way using the Track To constraint
I would like it to be able to rotate as well for accuracy, though. I’ve attempted to use the copy rotation, copying the rotation of the ik control since that’s the one thing rotating, but it prioritizes one or the other. It won’t track if it rotates, and it won’t rotate if it tracks, even if I switch the order around or change anything.
So that seems to be the way to not do it, so I’m looking for any ideas on how to do this?
Images included for clarification. Left image is not rotated at all, so obviously looks normal, then right is the control rotated, but the radius is obviously staying horizontal.

You can always change the influence of the constraint.

But probably what you’re looking for here is to just sandwich in a non-deforming bone with the constrant, parent the deforming bone to that bone, with no constraint on the deforming bone.

Then your deforming bone acquires the tracking from its parent, and you can rotate it off that initial position if you want.

A different thing you could is move the bone being tracked. If it’s deforming, make a new non-deforming bone to track. If you want rotation rather than motion, give it a parent at the elbow.