Now I just need to figure out how to make your normal auto-attack actually drain stamina. As it is, you can spam your regular attacks, with no limit. Ideally, I want (at 100 stamina) a Power attack to drain 75 Stamina. And a regular attack, to drain 30 stamina. This way, you can do upwards of 4 attacks, before your stamina is drained.. Unfortunately theres no way to actually prevent a player from not attacking when they have no stamina left... I might have to script this in, but for that, I'm afraid is going to require SKSE...
Well..wrong on both accounts but i didn't want to give advice about this part because changing it is a huge pain and I'm sure there is a better way. Anyway, here goes:
More racial edits, you need to flag all attacks as power attacks and adjust the stamina cost to your liking. This means changing every damn entry for every playable race, also you need to change the "powerattackchance" gamesetting to 100. (Not entirely sure on that part, but it's a safe bet if you don't NPCs won't attack as often as they should, I just did it to be on the safe side since creatures have their own powerattackchance variable that i did not have to touch). This will effectively prevent you from being able to attack or bash with no stamina. No luck on bows yet however.
I took it one step farther but this is where you really gotta be careful or you can screw your game up bigtime:
In the animations tab, you can edit the characters animations to add the condition of needing a certain amount of stamina or stamina percent in the powerattack roots.
Since I use highly modified race starting stats I decided to actually use both conditions like this:
GetActorValue Stamina > 50 AND
GetActorValuerPercent Stamina > 0.10 (AND)
In order to use this attack you need to have at least 10% max stamina and 50 stamina. This way you can't even use the powerattack unless you meet both these conditons.
Notice that 0.10 is considered 10% (annoying since this is NOT how all percentages are calculated, "GetRandomPercent" actually looks for the whole number, not the integer)
Lots of customization options here. Just gotta mind your step.
Again, no SKSE required

I would suggest asking around a bit before going this route, it can be risky, takes a while and is most definately not something you want to get into if you ever plan on releasing the mod to other people. But for me, it has been quite successful (as long as I load it last of course). My full "mod" have overwrites on everything from perk trees to leveled lists to movement types to original spells. If I ever released it as a mod for others there would be utter, complete chaos.
A bit tempting really, lol.