I think Riot has said somewhere that everyone on last year's poll is guaranteed a rework, with the remaining champions being Shyvana, Nocturne, and Mundo. Shyvana's definitely being planned for a rework, they said in the results. So these are the champions I would put in the next poll if those three are excluded:
- With Fiddlesticks being reworked, Shaco is now the one champion in League of Legends who has no clear place in the lore. We don't even know what he's supposed to be (granted, we still don't know what Jax is yet, either, but we know everything else about him so that mystery is justified). And as far as his kit, he's a mess. It's very clearly a 2009 kit and it only really works to troll the other team.
- Behold, the champion who has the worse base splash art in the game, and makes Leona's splash look like a masterpiece. Aside from an excuse to update that splash art though, Skarner's kit is very niche and could use several tweaks, though I think the core concept could probably stay the same. Visually, as well, he's one of the worst-looking champions in the game and it's so painfully obvious that his model is nearly a decade old. Lore-wise though, he's pretty solid at the moment, though we still don't know exactly what kind of magic the Brackern crystals have, how they're connected to the world's magic, what the Brackern were like when they thrived, etc.
- Voidborn lore. Enough said. We need it, and Cho'Gath is THE Voidborn, who just so happens to be the Voidborn with the most rework priority as well. His kit, while not as messy as some, is still not very clean, and could probably use some big changes, particularly his E. He should probably have more focus around his literally massive tank style. And visually is where he needs the most work, because that model of his is very old and not nearly as terrifying as he should look. EDIT: And, since he mentions Summoners in his voice lines, he's also one of the biggest priority champions to get a new voiceover.
- Of all the uncertainties in Voidborn lore at the moment, Corki's lore is the messiest and most confusing we have. Is he Piltovan or in Bandle City? Where did he make his plane, and where and how does he use it now? What other Yordles does he know well, and what does he think of other machinery using Yordles like Rumble and Heimerdinger? Visually, he also definitely needs updates to look more Yordle-like, and his kit, while not horrible, is not that clean, either.
- When Dragon Oracle Udyr was released last year, fans were happy, but clamoring for him to get a rework just because of how painfully outdated such a new skin looks on his model and animations. His kit isn't bad, but very basic, and we're not even sure whether or not it's lore accurate these days (with the viability of the tiger stance being the biggest point of contention; the other three stances reference Volibear (Bear stance), Anivia (Phoenix stance), and some turtle/tortoise demigod that's hinted in Nunu's short story (Turtle stance)). Visually, as everyone has said, he's probably the worst looking character in the game, now that Pantheon and Mordekaiser have been reworked, and his feet, while not total pizzas, are still small pizzas on top of blocks. Lore-wise, he's fine, but the voicelines definitely don't match anymore.
And if Riot does put the remaining three champions from last year's poll back into the mix, then I would say have those three plus Skarner and Shaco, since those two have the weakest kits of all these three, and that has been Riot's priority ever since after Kayle and Morgana's reworks.