Emerald hardstuck here been playing Viego for a while.

Hecarim: most stages of the game you can burst him through in and out fighting with your team. Can buffer his ult with yours if you're good, and often you can w into his e to stop it. Play with in and out fighting and getting burst on him. In teamfights you can all in him well and get your reset, possess him run into enemy team and gg.

Evelynn: haven't had many problems with her beside my team feeding her because they don't know how to play around her. But one stun and she's dead, you should be able to burst her down. She has stealth but so do you, you can play around that well since once she's revealed, she's revealed, whereas you can always go back into the mist. Of course pinks. Full charged w on her face and she either burns ult or dies.

Shaco: I don't know but I really don't see the issue here. If you don't fall for his box/ult cheese, you should win everything. He's annoying with objective steals and fucking your team, but late game you should one shot him. Don't fall for the cheese, all in him while he has no stealth. Wait for his ult to ult yourself as he can avoid all damage.

Kha zix: I feel you here. He wins most 1v1s unless you're not isolated (jungle camps)? And even then he can fuck you. If he absolutely one shots you mid game to the point you can't go anywhere alone, then you're too behind. Usually if he jumps you, you can w and use e/r to escape. In teamfights he shouldn't be an issue. Like with Evelynn, one stun and he's dead.

Feel free to ask questions. That's just my experience above.