I see. I was thinking about probably still using Sneak, but as you already somewhat answered, do you think using a bow while sneaking without any perks would still be a bit too overpowering? I'm also not a big fan of Illusion or Conjuration, and I'm definitely aware of how overpowering Enchanting and Smithing can be. Although I never considered your statement about potions. Hm. Would you suggest only using bought potions? Or possibly not using health/stamina/magicka potions at all, and simply fleeing if a situation's too dangerous?
I'm not sure I'd say anything in this game is too overpowering, the combat has very little to do with player skill, it's really a matter of choosing how you want your combat to play out. You can be nigh invulnerable, you can be extremely fragile, you can one shot everything or be a total gimp that gets one shot by most things. You can have all the strengths with none of the weaknesses, or vice versa. Regardless, it's pretty basic when it translates into actual game play. You choose a weak character you'll just have to play careful, kite around, hit and run, and take advantage of the bad AI more.
Sneak + archery is a pretty easy way to get through the game, I can't say for certain how it'd fare without perks though. The sneak skill doesn't rely too much on perks, even less when you're using archery so you don't have to get too close. Archery won't do very much damage without perks though, and you'll have to spend a lot of time running if you don't have power shot to help prevent enemies from getting into melee range.
As for potions, it's really up to you. You can limit yourself to a certain number per fight, you could use restoration instead, you could only use them when your character is out of combat or in a safe enough potion that you'd be able to drink one in real time, etc. etc. Only using bought potions wouldn't be a major limitation since money is easy to amass in this game. I personally didn't use potions just because I'd hate going in and out of my inventory in combat plus I feel instant health potions are a terrible game mechanic and a crutch. Restoration is decent enough.