Rings and amulets sound an awful lot like magic to me.

If I were going to try this, I think I'd use a Dunmer, Thief birthsign, Combat specialty, with Strength and Speed as attributes. The Dunmer is resistant to fire, and the low-level Daedra use a lot of fire. Dunmer are also fast. Thief birthsign boosts Luck, Agility, and Speed. Combat boosts Hand2Hand and Athletics.
I would want Hand2Hand and Athletics as majors. I would build up Sneak to Apprentice level in the tutorial, by sneaking around the non-hostile rats, but would keep it as a Minor. I would make Alchemy a minor, but spam it up to at least Apprentice as soon as possible. There are a couple of easy early boosts to Hand2Hand:
Spoiler The skill book outside Vilverin, and watching the two fighters sparring outside the Arena.
I would try to rush through the MQ at as low a level as possible; it will get very difficult to do this at high level.
Question to ponder: Does praying at a wayshrine or temple count as magic? If not, this is one way of healing and buffing. Otherwise you're stuck with Alchemy.