If Canaqua is going to be the primary caregiver then she should get to choose the dog. However I think that her DH is entitled to some input. If he can’t stand little yappy dogs it isn’t fair to get a little yappy dog. He has to live with the dog too.
His concerns about size and hair are fair. I can see certain breeds being a deal breaker.
I don’t think it is fair for you to just go get the dog when he has clearly indicated that he does not want this dog.
See if you can get him to meet the dog. Maybe once he meets it he will change his mind.
If you are truly concerned about the dog can you agree to foster the dog, with DH approval and be willing to put a good effort into actually placing the dog once he is neutered and a fine upstanding dog citizen?
Can you have a discussion with him to see if he is objecting to this dog, the timing etc…? Have you asked him what he envisions as your next dog- age, sex, breed, energy level, size?
I think you need to compromise here a little. He has to live with the dog too. I do think he should get some input but final choice should be yours if you are the one doing the care and training and he is not.