I agree with everyone else. In my opinion, health tests are one of the most important things to be done, with registration being the least important. AKC does not have good registration policies anyways, and often registers mutts as purebred dogs. Are your dogs pedigreed to show what airedales are in their background?

I did a little research, and airdales should have a few certificates in order to support the health of their offspring. CERF for eyes, OFA for hips, and their hearts and thyroids need to be cchecked too, as well as their skin should be regularly checked by a veterinarian. Have you done all of this before you considered breeding?