In this case, I suspect that the governor might appoint himself. It would give him a chance to get his name in the public. Based on commentary within the state....some people think a quick election would not be beneficial for Gov Ducey if he did intend to run.
Odds on McCain’s wife? Just about zero.
According to the NYT the McCain clan is pushing Ducey to appoint Cindy. And Ducey once worked for her family’s Budweiser distributorship