If you can get it pass ban phase, the new Malzahar rework works wonder against Assassins. Someone else already suggested Vlad, and I guess Swain is not too bad. All 3 of them are relatively tanky for Mages, Swain and Vlad have good sustain (post-6 for Swain), and they pay it with their medium-short range, but it's not really an issue against Assassins who want to come in melee range. Not sure if it works well versus Zed specifically, though, because of his medium-long range poke. Lissandra is probably good too, with her self-ult to heal her+prevent Zed's mark detonation.
As for Azir, I suppose his ult can let you disengage when an Assassin wants to all-in you, but I'm not sure it's very effective. And if you want to pick a straightforward champ since it won't be your main, just a counterpick, I suggest Ahri among the 4 you proposed.
Regarding Yasuo, I guess anything that can outrange him and poke him down so he cannot abuse his shield is good. Sure his windwall is annoying, but it has a far longer cooldown than any of the mages you cited. Don't try to all-in him and put your whole combo in his wall, that would be stupid. But use just one skill at a time and get him low. This should work with Cass, Ziggs and Jayce, at least, maybe Lux and Velkoz, among the champs you already play.
Now if you want something good against both Yasuo and Zed at the same time... I guess I'll propose Vlad/Malzahar/Swain/Lissandra again. They are maybe not perfect against Yasuo, but they shouldn't suffer too much, so it's probably the best compromise.