If every champion in this exercise gets exactly 1 change, no more, no less, it would mean basically the higher tier ones get a single nerf and the lower ones get a single buff, with middling champions getting a lateral change so let's go with that as the premise
Q cooldown 14/12/10/8/6s -> 17/14.5/12/9.5/7s
Q true damage moved to a part of the Charm debuff
Q cooldown increased 1.5s -> 6/5/4/3/2s
E shockwave interval 05s -> 0.4s
R disarm replaced with a channel disrupt
R mana cost/s 40/50/60 -> 50/55/60
Q cooldown up, reduced by 50% if Q kills a minion: 4s -> 7s
Q mana cost removed
R cooldown 110/90/70s -> 90/70/50s
E cooldown 19/18/17/16/15 -> 20/18/16/14/12, but Azir will only dash to the location of his soldier at the time of E cast even if Q is cast after
{{champion:432} Shrine (W) prep time 10s -> 10/8.5/7/5.5/3s
Q missile speed 1800 -> 1300, 25% cooldown refunded on hitting a minion or monster
E AP scaling 45% -> 60%, deals 50% bonus damage to minions and monsters
W bonus resistances flat and scaling: 10 / 14 / 18 / 22 / 26 (+ 10 / 11.5 / 13 / 14.5 / 16% ) -> 18/21/24/27/30 (+21%), but allies only receive two-thirds of these bonuses (12/14/16/18/20 +14%)
E mana cost 75 -> 80/70/60/50/40
Pasive Shield: adaptive -> universal, cooldown 16/13/10s -> 18/12/8s
W nerfed early, buffed late -- cooldown 24/22/20/18/16s -> 25/22/19/16/13s; dps: 20/25/30/35/40 (+ 15% AP) -> 18/26/34/42/50 (17.5 % AP)
Bonus health per R stack: 80/120/160 -> 100/130/160
E resistance shred changed to 1/2/3/4/5% from flat 1 / 1.375 / 1.75 / 2.125 / 2.5, max stacks 8 -> 5
E armor pen changed from passively 15/20/25/30/35% -> 3/4/5/6/7% per stack of Hemorrhage, but now E applies a Hemorrhage stack as well
W base shield amount 40/55/70/85/100 -> 40/60/80/100/120
E bonus AD 40/50/60/70/80 (increased by up to 100% based on missing health) -> 40/45/50/55/60% of total AD (+1% total AD per 1% missing health)
Auto attack windup decreased, and base attack speed 0.679 -> 0.625, basically to make weaving additional autos between axe catches easier while decreasing his general dps
I'm also realizing how long this is going to take to go through every single champion so I'll just do the ones I play or find most frustrating to play against for the rest of this post
W bonus resistances 10% -> 10 / 11.25 / 12.5 / 13.75 / 15%
E execute damage 8% +0.5% per passive stack missing health -> 4/5/6/7/8% +0.75% per passive stack missing health, slow 50 % for 1s -> 30/40/50/60/70% for 0.5 / 0.75 / 1 / 1.25 / 1.5s
Q deals magic damage equal to its enhanced auto damage to enemies it passes through
W arrow indicator appears 1 second sooner, but Evelynn gains 30/40/50/60/70% bonus movement speed when moving toward the target while W primes
base movement speed 330 -> 335
E cast range 615 -> 665
W doesn't block projectiles until it reaches 225 range
Normal turrets take the same modified damage as
plants from champion attacks and abilities, health against non champions increased 150-575 -> 200-600, turret mana cost 20 -> 60/50/40/30/20
blind duration 1.5/1.75/2/2.25/2.5s -> 1.75s mana cost 70/75/80/85/90 -> 80/85/70/65/60, cooldown 8s ->12s
Grey health ticks down if Pyke remains in vision of enemy champions without taking further damage after 5 seconds
Q damage 65/100/135/170/205 -> 45/75/105/135/165, Q enhanced damage 100/150/200/250/300 -> 150% normal damage