Throw Q for damage, kite back. Move so that she is not able to damage you and remain near her minions. Hopefully your using smart cast, spam W constantly at the area she is in, again you need to position so she cant hide in her minions. Land the W when she breaks stealth because your constantly imputing invalid commands until the second its able to target her, Throw out another Q.
If she has a minion wave I guess whats left as an option is You can try to stack Runes for the Q shield to midigate some damage but your gonna need to hit minions with E casts. Ideally your not gonna want to be in a position she can stay in minons for safety and still damage you. Try to take advantage of her short range to position her away from safty.
Honestly unrelated to akali I wouldn't recommend Ryze ranked if your not duoing or in flex. People don't take advantage of his R, and that sucks a lot cuz you could cast it fucking flawlessly 100% of the time it wont matter if your teammates derp. Also kinda feels like he just has a lot of awfull matchups .
Overall as ryze don't bother fighting her in shroud, it will interfere with your ability to combo well, when she lands the E on you Open with a Q when she is dashing in and try to get the EW off befor she connects with you. Shes gonna have passive, W, Q, trigger passive, then might R if your low, passive Q R and kill ya.
If you don't use smart cast, you should. At the very least use smart with indicators, I like being able to hold and aim abilitys, but a single key input to spell cast will SAVE YOUR ASS IN FIGHTS!
Its pretty easy to land point and click on akali with smart casts point when shes under vision that gives you indicator of where she is at, just spam the ability until she breaks it. Don't make it a reaction game, be prepared in advanced, constantly throw down that CC so it will hit the moment she becomes a target.
Edit. Also I think morde does a good job fucking her up in lane and can feel really oppressive for her. If your looking for a pocket counter that's been mine and im not that great of a morde.