Well I decided that I would make my first Argonian character ever. I've only ever seen my brother play them once and my sister play a Khajit. But I realize that when fighting with a blade in Skyrim that they sound like the humans the Breton or the Imperial during a power attack. And I strictly remember in Oblivion that they made more of a beast noise.

So I was considering is punching and box enemies a viable way to go in Skyrim?

Sure, why not? Get the Gloves of Pugilist, and you're ready to go.
Might want to keep the dificulty at Adept though.

Yeah, it's not half-bad and you'll get rewarded with some awesome killscreens. Khajit does a bit more unarmed damage, but argonians get a bonus too.

Yes. With smithing/enchanting and a shield in the left hand (swap out shield w/ heal spells when/if needed), it's very possible. You'll just kill slowly at higher levels.
The shield prevents kill-cams, but increases survivability. Shield also swaps with lefthand spells easily.

Awesome stuff. I just watched my Argonian flip over someone and do some like wrestling move. Pick them up, and then slam them back down. Woah woah. Cool stuff.

I would have been boxing... but then they removed hand to hand

Also, don't forget that if you put points into Enchanting then you can disenchant the "Gloves of the Pugilist" and put it on something else.

Combine this knowledge with thePerk in the Heavy Armor tree that allows any gauntlets worn to do their Armor Rating as Damage... + the effect of the pugilist enchantments... you get the idea.

Argonian looks bombdiggity in the Hammerguard clothes.

Give it a go. After changing from PC to XBox, I had trouble recognising if I had properly set my weapon in hand.

Facing the first Giant Spider -fixed fight in Bleak Falls - I spent half the fight punching the spider. When I finally got my weapon in hand, the spider went down much more quickly. The look of shock on the spider's face when the first 10 punches landed in a flurry .......

A LOL moment.

That does sound really cool. I may have to try this out. I've never seen this wrestling move.