I think what the OP wants is already in the game in some avenues. Morgana is the dark mage, who shoots bolts of dark magic etc. Twitch and Cassiopeia are the two who operate on poisons and diseases.
But these are really what makes the iconic "witch." Hell, not even the green skin that the OP mentions is iconic witch. That's strictly based on the Wizard of Oz.
The witch we ACTUALLY need is a much different character altogether, someone who hasn't been done before in the game.
First of all, we don't really have an old woman in the game, at all. There are technicalities, but Riot has always magicked away their age to make them young and beautiful despite their supposed old age. We need a hag. A crooked, withered old woman with gray hair, a slightly harsh, raspy voice, wrinkles, with gnarled knuckles. She could use a cane or a walking staff, but overall, we just need an elderly woman in this game. It's been 10 years. I find it wild that Riot has not made ANY character like this yet, especially since fantasy settings are the perfect place for those characters. If the Netflix Dark Crystal show can make Aughra a fucking badass old hag working to undermine the Skeksis, Riot can make their own badass old hag.
Secondly, traditional witchcraft is generally based around familiars, invocations, incantations, and sacrifice. Fairy tale witches operate on a different set of directives, often using trickery, transmutation, and potions to work their magics. We would do well with a traditional witch, who would have some way of either sacrificing her own HP to make crazy shit happen, or channeling spells and effects through some sort of familiar, akin to Lulu or Orianna, or creating circles of magic/protection that allow them to save allies from harm or cast their own magic more effectively. Circles of magic/protection would honestly be the best route, as I don't think any champion in the game really operates like that. The closest we have is Taliyah, who's inhibited when standing in the zones she creates. The witch could use HP sacrifice as part of her spellcasting as well, to really seal the deal. Overall though, we need a real sort of witch hag, not a storybook/pop media version.