You need the attack level to wield the corresponding hatchet. For example, if you want to wield a mithril hatchet, you'll need an attack level of 20. Should you not have that attack level, you would not be able to wield it; however, at a woodcutting level of at least 21, you'd be able to use it, if it was in your inventory. To sum up, you wouldn't be able to wield a hatchet higher than iron as a skiller, but with the appropriate woodcutting level, you could use it still.