Ezren appears to use a hanbo ("a staff less than a yard long, often carved to look like a walking stick"), even though he was always statted as having a club.
So are wizards proficient in the hanbo or is this an art directional coincidence?
Art directional coincidence. That and the fact there are only so many differnet pictures and names you can use for a stick before you have to admit it's a stick.
"Club" is a broad term.
I would say this for once. You could probably use a hanbo, but only get the club-stats for it.
Hanbo is a specific kind of staff used in eastern martial arts. If you look at these pictures here or just google "hanbo", you'll notice that while the description given for the hanbo kinda fits Ezren's stick, it doesn't exactly match any of these pictures.