This one is kind of a bit far off base. The heads are allowed to have simple stun items, because they are heads, and they need to stay protected. An axe is not a stun tool, it is a tool meant for breaking down windows. An atmos tech is not a head. The axe is most often used as a weapon, and almost never used for what is meant to be used for. There are almost endless reasons to not carry it around, and pretty much only two reasons to carry it around.
Thing is though, carrying it around (and not stabbing anyone to death) is no reason to stun, cuff and brig.
In nearly all situations, its a case of "Put the fireaxe back when you can."