What about the current Lt. Governor in Az?
Google just taught me that Arizona doesn't have a Lt. Governor. When necessary, the Secretary of State takes over the Governor's role. The current SoS is Michele Reagan (no relation to the former President). She's a pro-choice Republican and supports same-sex "marriage".
Some writer suggested Ducey's chief of staff, Kirk Adams, as a reasonably conservative placeholder until someone, perhaps Ducey himself, is elected. Ducey could appoint himself, but that would be unseemly, and I suppose it would elevate Michele Reagan to Governor.