Zed while portrayed as a villain, does things he genuinely believes will improve the kinku tribe. I don't think hes a bad guy. We don't know what he saw with shen's father, so he could be a hero for all we know.
Talon wishes to be the best, for self improvement.
Kat wishes to please her father.
Rengar and khazix both want to be the strongest, so they hunt and train/evolve
Qiyana is a brat, but she isn't evil per say.
Akali wants to do do the dirty work that the kinku order doesn't do.
Kayn just wants to be the leader of the shadow order
Kassadin is just a father who escaped the void
Kaisa is a legit defender of shurima
Vayne purges evil
i probably missed a few assassins, but pyke? Pyke legit kills because he has spite and rage. He doesn't have a goal in mind, he wants to kill everyone in bilgewater for self vengeance. "But its just those who betrayed him on the ship!" you might say, but his mind is so warped and twisted that he sees everyone in bilgewater as guilty for his death. So if he sees anyone in bilgewater, he "recognizes" them, then their name magically appears on his list.
All the other assassins have a bigger picture that isn't just all cons. Pyke just wants oblivion.
EDIT: I should say that there are a few who could be considered chaotic evil, now that i read some comments, like Evelynn, nocturne, or shaco. However, while evelynn might be chaotic evil, I don't think noct and shaco have their lores fleshed out enough to say where they stand on the evil spectrum.