Like a monk or some other martial artist. Lore friendly, of course.
I doubt it very much. There are just no skills to support that kind of character, no weapons like gloves or knuckles, and you would be severely gimped not having a weapon. I wondered also when I found Brawlers Gloves, maybe it was intended but not implemented.
You can try. Tank up and don’t use weapons and see what you can do. I imagine it is going to be painful and you will wind up relying heavily on spells and retaliation damage. Ultimately your damage is all about the modifiers and not so much the weapon. Maybe you can get tanky enough and strong enough to one punch most enemies. Spoiler, its going to be slow and boring.
Edit. On second thought, you wont make it out the gate. Bare fisted you can’t do enough damage to dent the first zombies you encounter.
From what I can see, the world of Cairn seems to lack an order of monks like you decribe. So for lore, there wouldn’t be a point in having such a character. Where would he have acquired his knowledge of such martial arts in the first place?
We know the occultist gets knowledge from the witch gods and their orders, similarly the nightblade assassins are like Ulgrim and the shaman are from mogdrogen’s and ultos’ wild magic. Just to name a few.
It would be cool though, perhaps a new mastery one day 
I would love to play a monk like class. Monk was one of the few things I did enjoy in Diablo 3. Was one of my favorites in Diablo 1 Hellfire. Getting all the animations done for that with the whole kung fu brawling style would be quite intensive I bet. There are many ways to learn martial arts without having to join a Monk order. Monk is just an Archaic title.
On top of that I’d like a mastery with Envenom Weapon, Poison Bombs and some healing/pistol support. With a proper pistol default attack with some WPS’s. Maybe an Alchemist of sorts?
Those two masteries and this game would be Ultimate and in my regard considered Complete from development 
There’s a mod for that which, while not D3 Monk style, it is fists based…
looks weird though. its just melee animations. but instead you hit in the air since the weapon is made invisible somehow. It is a start… Was thinking about using an invisibility potion in combination with the illusionist. That way you can use weapons for stat bonusses, but not see the weapon in actual combat.
Like, they will of course add knuckles and some fighter gloves, make new animations for the class, etc.
Well just like the new expansion, a new faction is coming, new items, new classes, and I don’t think that is impossible, just unlikely to happen. Or not.
fighter based mastery is not in the expansion