If you need to donate to your wife and aren't compatible, separate from the NKR vouchers, there are "kidney exchange" programs where pairs of people in that sit

If you need to donate to your wife and aren't compatible, separate from the NKR vouchers, there are "kidney exchange" programs where pairs of people in that situation are matched with each other. So you'd donate to someone else, and at the same time someone would donate to your wife. Actually calculating the match among all those pairs is a fun NP-hard optimization problem.