A pugel is the weapon you use on the balance beam, a form of the combat ring in player owned houses.
It has no wield option, but will automatically be wielded when standing on the balance beam, although a glitch currently renders them invisible until the player steps off. When the player steps off the balance beam, they would appear to be wielded, but the pugel is actually still in the player's inventory and all their combat would be the same as doing it barehanded.
A pugel stick can be obtained by building an extra weapons rack.