I used to live in tempe and commute to phoenix, briefly passing through scottsdale. Just moved to ahwatukee. Still bike to work and my route is 70% the same.

I take mill most of the way and pass thru Papago park on the crosscut canal. People have recommended I take priest or college instead. Mill can be a bit busy, but it works for me. Has a bike lane. I'd guess rural is a bit busier, but I've wound up on rural some mornings and it's been ok.

Originally, i tried to work the western canal into my route, but wasn't worth it. Had to go too far out of my way.

There's a couple jogs where there's no bike lane. In that case I usually hop on the sidewalk if there's much traffic.

Bottom line, commuting from scottsdale to tempe shouldn't be a big problem.