Quick answer is, you can parent your walker's hand to the prop and the prop to the dog's neck without too many difficulties. And you can create a hybrid conforming/dynamic prop by selecting a single 'bodypart' (as it were) to use in the cloth room - in your case, the lead between the dog and walker.

I think I would choose to make the dog's neck parent to the leash and then parent it to the walker's hand rather than the other way round, though - in my head, having the dog as the overall parent would make it feel like the dog was taking the human for a walk...

... but then again, I've seen that happen more than once! :)

JonTheCelt