If Zunesha was someone with a Elephant Zoan Devil Fruit, wouldn't they get super weak from their legs being submerged in water? I mean, I guess that would explain why he always looks so sad all the time. But, I think he just has one of those faces. (And, y'know...the whole "cursed to walk the Earth" thing.)
The rules for exactly how much water Devil Fruit Users have to be in can be a little tricky. And Zunesha does have long legs, so he's not in THAT much water, proportionally. But, he has been in the water for centuries. If he was a Devil Fruit User, I don't think he could do that, at least not for that long.
Plus, yeah, the Voice of All Things points to him being a animal. If he was a Zoan, he could just talk. Unless he's actually speaking another language because he's been alive that long, so he can only communicate with modern day people through VOAT.
I think most of the proof we have says that Zunesha is just a very big elephant.
Part of me does wonder if Zunesha could be hiding a "Abyss Mark" of some kind on his back, underneath the city he's carrying or something. Something like that might explain his "curse". But, that's just a random thought. It'd be an interesting twist, but we don't have any proof for it. It would just be interesting if Imu or one of the Gorosei or someone was the one who "cursed" Zunesha.