A lot of the answers would have been what I would have replied with, but since you want "sucky" there's a lot you could try. I really think Tannehill or Dalton would be best but Tannehill can run and Dalton's stats may be a little too good.
Why not try finding a backup or something? Matt Barkley seems like a good choice. His short and medium throw are decent but his deep throw isn't good and he is slow. Mike Glennon? Colt McCoy? Heck, I'd even try Carson Palmer or get a free agent or make a trade for a QB and bring him to Arizona.
Arizona has Fitzgerald, Michael Floyd, and Andre Roberts. The run game is not very flashy so I think that's a good situation. Otherwise just go with Tannehill and don't run.