This thread is your friend.Simple answer is yes,
if you are using
melee moves.
The fist icon means it is unarmed move. You
can use unarmed moves with or without a weapon equipped, like an anytime. You
cannot use melee moves without a weapon equipped.

The melee moves will tell you that you need a weapon equipped. Many of the melee moves 'attack weight' and 'attack damage' come from the weapon's stats, not your melee skill.

However some of the melee abilities do use your melee skill, indicated by the melee icon.

If you haven't been fighting a lot of animals yet, you might not have very many abilities. As you kill more and different animals, you will learn more combat moves. Some will be unarmed, others will be melee. You will probably use a mix of both depending on what you are doing.