1) Both my Demon Hunter and Wizard with weapon unequipped does not give me the default 'Punch' melee skill. However it works for my Babarian and Monk.
2) I tried to waste my hatred and it works, but I have another friend using Demon Hunter and by removing his weapons, the 'Punch' skill is displayed for him.
Edited - Ok under options -> gameplay -> make sure elective mode is selected. then click and hold on the 'left-mouse-click' skill in your skill bar and drag it out, rmb to remove your weapons!