First I want to note some points about your chosen Champions
As most of us forum dwellers already know, Caitlyn already has some explorations flying around by the now new company member Riot Hylia, which even can be seen on his ArtStation. Vlad Bacescu also did some exploration on her and also did some work for Riot already. Can't wait for her having more of a victorian/Sherlock Holmes vibe.
Just needs some modern models and maybe some reimaginations on skins (Jailbreak & Hired Gun). His classic just should look exactly like in the splash and he is overall very iconic.
Riot seems to already embrace his current theme by looking at the art of ''Where Icathia Once Stood'' and I just would like to see him getting a small amount of armor/magic penetration or % health damage added to his kit to be more viable against tanks.
LeBlanc is a complete visual mess and doesn't fit anywhere.
As already pointed out by others in this thread, Quinn without a doubt needs to become a Raptor Knight. it is just a logical consequence.
Just needs his rig/model/textures updated with help of his legendary skin, otherwise he is fine as he is. Fits in the region and is iconic.
New model & rig with more of a noxian assassin vibe in combination with some skin reimaginations will be enough, I guess.
I would like her and Lucian be more related. Members/Agents of the Secret Holy Round Table of Demacia with different fields of expertise (Lucian the undead & Vayne dark magic creatures), Vayne sharing a similar (but still unique) uniform design like Lucian, but keeping her hair & fitting glasses.
Yi is completely fine visually and just needs some kit changes combined with updated VFX for example Assassin (purple), you probably also have seen the Noxus Poppy thread.
Completely disagree with Tryndamere. His kit is the definition of toxic and falls in a similar field like Pantheon on this matter. He needs much more work, with his Ultimate/Rage theme staying. Otherwise it would be cool to see him and Ashe be updated back to back. I also would like to see Olaf being his right hand.
And to dive deeper...

What about these?
Annie recently had a cinematic shown her with completely different, much more noxian childlike looks even and her current visuals fit nowhere into Runeterra, but in a modern world. Olaf falls under the same category as Pantheon & old Gangplank. Ashe looks nowhere fitting for the Freljord environment in terms of appearence. All of these names are fine as they are and just need their visuals updated. From what I figure out.
Kog'Maw could use the new foundation of the Void, doubling down on the larvae ''Some legends suggest that, when they first emerge into the Runeterran air, the Voidborn are generally pale, fibrous and flexible. As they age, sections of their form harden into a darker, shell-like chitin, which can become strong enough to turn aside almost any weapon.''.
Vladimir & Veigar also could use some more regional definition, Vladimir looking more like an actual noxian nobility. Veigar is a bit of a mystery to me.
Rumble fits perfectly to Zaun, a little less to Piltover and his gameplay is also completely fine from my current view.
Malzahar & Orianna would just be nice with modern rigs and the outdated skins getting a lot of attention.
In terms of especially minor GU mixed in I clearly see Wukong, Janna, Blitzcrank & Jarvan IV.
Jarvan recently had a great concept released on the universe map page, how he actually looks and could use a small modernization. Blitzcrank could get a similar update like Ezreal mixed with Akali (in terms of progressed story - he gets upgraded by let's say Heimerdinger with the help of Ekko... the 2 fit for buddies as seen in the The Climb cinematic - Ezreal in terms of being a little more than just a hookbot).
A while ago Rioters said, that Wukong ''is almost there'' in terms of gameplay and just would need a bit of him changed, to have an actual cohesive kit. Also it would be sweet, if he would look much more like a mixed Vastayan, with the main focus on monkey.