Just a thought about how it could be implemented without creating new skills and how it could benefit both Stamina and Magicka play styles.
Unarmed Skill Line
Passives:
Unburdened:
Increases your movement speed by 6%/12%.
Toned Body, Honed Mind:
Increases your Stamina and Magicka Recovery by 150/300.
Iron Will:
Increases your damage done by 6%/12%.
Dexterous:
Increases your Critical Chance by 650/1300.
(Select One):
Tempered Fists:
Increases your unarmed light and heavy attack damage by 25%/50%. Fully charged heavy attacks stun enemy targets for 3 seconds and grant Empower for 20 seconds.
Enchanted Hands:
Your unarmed light attacks become projectiles that deal X/X Magic Damage. Your heavy attacks channel a beam of energy that deals X Magic Damage over 2 seconds. Fully charged heavy attacks restore Magicka and grant 2/4 Ultimate.