Depends on how exotic the weapon is.
Every champion has kind of "his" thing. Lux has lightmagic, Heimer has turrets, Thresh has chains and Sivir has her richochet thingy.
It probably doesn't make a lot of sense to make another "mechanic" champion that's about turrets or another fencing champion, like Fiora. Similarly, it's very hard to have two champions about the same thing (fire, with Annie and Brand), without taking away from each other. Fortunately, Annie has Tibbers, so she doesn't solely depend on fire for her identity. You could also take Zilean and Ekko to have two champions using similar mechanics, but fortunately, you can do more than enough stuff with time, to not make them bump into each other too much.
Spears and swords are very common on many champions, because they don't make up a lot of a champions identity and can be used in versatile ways (compare Xin, Nida and Kalista).
However, exotic weapons usually aren't as versatile and can usually only do very specific things. They will very likely take up so much of a champions kit, to make the champion feel like using the weapon, that it would also make up a huge part of the identity and can't be put on another champion, without crippling the character of either.
I only know fanweapons as deceptive and deflective melee weapons, and any attempt of putting them on a champion would probably revolve around that. I can't think of a way to make them work on a ranged champion.