The Cane is a melee weapon. It looks like a walking cane because it is one, and Getty starts with it.
It deals good damage, but has a penalty for attacking lesser monsters, dealing only half damage to them. This discourages attacking them, as if it weren't for the penalty it would make short work of them. It thus is focused towards hurting larger foes, though close combat with most greater monsters is still a poor choice on your part.