Hard to say. But I guess it's safe to assume it wouldn't be anything too fancy or complicated like some people have, Byakuya as a good example (like too fancy for Zaraki, for Byakuya of course not).

However, Zaraki is a genuinely very good fighter. So, I don't see why he would need a huge axe or hammer. They don't fit a fighter who also knows how to rely on skills, not only sheer overpowering strength. Especially since Zaraki at least used to think zanpakutou is nothing more than a tool, and the power lies in the user.