Hail of Blades is also a pretty good choice for Azir.
I think Glacial Augment would actually be a good keystone for him too, but it takes a bit of setup until you get GLP-800. Soldier's attacks don't proc the passive slow, but if you summon a soldier AWAY from the enemy, attack with a basic attack from Azir, then Q onto the target, you can get a few good attacks off. With GLP-800, you can just toss your abilities out like you do normally, and use the GLP active to apply the massive slow. Also since you are taking Inspiration in your primary path, whichever secondary path you take will give you the greatest Attack Speed or Ability Power possible.