The hook comes handy when Three Finger attacks the prisoners as it is easy to stab with it.
When he is fighting Chavez it comes handy because when he is about to swing the axe on him Three Finger takes the hook and drags it across his arm and stopping at the wrist. Chavez is exhausted and is lying on all fours and Three Finger takes the hook and stabs him in the back.
The hook comes handy for not Three Finger, but the survivors. When the car Three Finger is on crashed he is slung away and drops his hook. The survivors thought he was dead but when Nate Wilson sees Three Finger charging at him he takes the hook and stabs it through his chin coming out from his forehead killing him.