Personally im a big fan of fiddlesticks here. Sure, shaco can go invis, but with a tiny bit of intuition you can just keep on going with your ult and steamroll him. And if you've got a large amount of hp due to succesful laning and some hero kills under your belt, you can try and just drain him out when he tries to melee you. Turns out that simultaneously increasing your hp and decreasing the opponents hp against a melee dps is pretty good for staying alive. If you can manage to heal yourself for about half-3/4+ of the dps he's dishing with his drain, you should be fine until hes in range to terror/darakwindslap/ult away in a quick couple seconds.
Solo mid as fiddles versus ez is a blast because you can constantly harass him with dark wind. He's annoying to try to drain, but terror will make ez an easy target for you and your allies to pick away at. Keeping flash ready as much as possible is good if you think he'll try to throw his ult your way and you're not in the same lane as him.
Honestly, I think just playing smart with any character is the way to go against Shaco and Ezreal. Don't feed, try to stop your teammates from feeding, and they'll be little more than nuisances you get to slap around.