You are correct.  Waddell is not a city, it is an unincorporated town.  However their mailing zip code is 85355.  https://www.unitedstateszipcodes.org/85355/

It's considered a city by US Postal.  Also, if you ask anyone living at any of these houses, they'll tell you they live in Waddell.  Is there a way to recognize both? 

