Err, not really.
**Master Yi **holds his blade with 2 hands but attacks using 1 hand. There is a reason for that because he is modeled after Chinese sword arts (EDIT: Not swords, Dao, they are 2 different things there) which use their blades with 1 hand primarily.
**Garen **does hold and attack with his sword using 2 hands.
**Darius **holds his axe 1 handed because he is holding the axe near its cutting bit, making it unnecessary to to use it with 2 arms. He does use 2 hands when serious, such as when he is dunking.
**Kayle **is not human, and possesses magic properties by default, thus her strength can not be compared to human standards.
**Mordekaiser **is a wraith who is trapped inside his armour either by choice or as a result of an external party's intervention. His strength is thus also not comparable with human standards.
**Riven **uses circular motions a lot (her Q) to keep her blade in momentum once she starts swinging it. Not to mention it's a magic infused blade, and it's already broken to the point of having not much else outside of the hilt.
**Tryndamere **is a barbarian noble. It's his personal preference to smash things with his impossible sized sword while using only 1 hand, as such you always see him dragging his sword around instead of carrying it, and requires full body action to swing it properly.
**Sion **is a modified human corpse + technology + magic construct, his strength is not meant to be parallel with human standards.
**Renekton **is an "ascended" human, he has the physical capability to swing his big thingy with 1 hand.
etc etc
Also, what's wrong with swinging big weapons with 1 hand? This is a fantasy setting after all.
Not to mention if the toons we're playing are not some kind of super human/entity by default, I doubt they would even qualify to serve as a Champion to begin with. Using 2 hands to hold their weapons is generally a choice/preference for these people, and not a must like your average joe.