Here's the plan.
He likes to hunt and he occasionally shoots guys while he's hunting.
That's documented.

He has connections world-wide.
Default settings there.

He contracts with the Chinese for a hunt.
The game, you guessed it....the Chinese find convicts that are suitable donors and the hunt is on.
Before you know it, Cheney is back in the US hunting quail with his new Chinese heart. He also opens a chain of Chinese fast food restaurants.

Edit:
After going through several donors, the Chinese wise up and put a flak jacket on the last one.