These things can be clearly spelled out in a will. No reason to have a hostile ex-wife involved.
In a real-world situation, the will only matters if it is seen. If you were just in an accident, can be considered brain-dead, have the organ-donor box checked on your driver's license, and your available next of kin says "go ahead", then that might be it
I stand by my original assertion that (for some disfunctional families) having a cash incentive might not be good for the prospective organ donor