Is an assassin ineffective without improved weapons?

I'm planning to make an assassin and won't improve my armor since I don't intend to get attacked. I roleplay a Khajiit assassin that doesn't know anything about smithing, so I don't want to smith at all.

I don't know if the daggers sold by NPCs will be enough to one-hit people with the 15x perk. Does anyone know anything about that?

I do intend to get a Fortify Archery amulet and ring since they increase a dagger's damage, and I also intend to spend points on the 1h Armsman 5/5 (but won't spend on dual-wield.)

Is that enough to 1-hit-kill bandits on my level, draugr, etc and do at least good damage to bosses ?

You will probably be vulnerable in open combat against stronger enemies, but this is a perfectly reasonable build. In fact this is my build at the moment (sneaky assassin with daggers and archery) and it works a treat. I am just about able to 1-hit kill a Frost dragon and am level 33 or so.

Increase sneak as much as you can, and early. This will let you more easily a) stay hidden and alive and b) get those delicious sneak attacks we all know and love. Anything to increase sneak/backstab damage is really useful, including, as @Rodrigo Guedes said in his answer, joining the Dark Brotherhood and Thieves Guild (you get some great armour if you follow the latter through to the end).

I haven't got any smithing to speak of (20 or so) and am using Mehrunes' Razor (highly recommended as it can occasionally 1-hit kill, saving you some hassle) and the Blade of Woe, which is useful to claw some health back mid-battle when needed. Remember that when you're lower level and using unenchanted daggers you can still improve them a little bit!

I've also found archery to be incredibly useful. It can do a ton of damage if you level it up and use good arrows, you can start doing damage at enemies that are rushing at you once you've been spotted (the perk that slows down time when you draw is a lifesaver) and you can also increase the sneak attack damage to 3x instead of 2x. That's not as much as 30x but you don't need to be as close! :)

Also, don't forget your Thu'um. Slow Time is great for positioning yourself or running away, Throw Voice is great for getting targets into backstab-friendly positions, Marked For Death is great for extra damage in open combat and finally Aura Whisper is an absolute must - cast it as you walk around in a new dungeon and you will never be taken by surprise! I think I use this more than any other shout.

Happy stabbing!

At 100 one-handed and 5 Armsman you will do 300% base damage of your weapon. Supposing you find a daedric dagger, that's 33 points of damage, or 495 damage on an x15 sneak attack, or 990 points of damage on an x30 sneak attack (DB gear bonus). Should be enough to deal with most regular enemies, heavily armored enemies might survive an x15 attack.

Fortify Archery only boosts dagger damage if it's from a potion, though, and that bug may have been fixed.

Not necessarily. But you will need a really good weapon. I recommend Mehrunes' Razor: it can kill instantly any enemy. And it's very well suited for an assassin (in terms of role playing), because it is a dagger. Additionally, you may want to join the Dark Brotherhood or the Thieves Guild to get their set of armor.

I'm a level 49 wood elf thief/assassin and have never ever participated in open combat because of my bow. If you get a decent bow you will never be seen as long as you load up on the appropriate perks. I have ebony daggers and sword and a shield that I've never had to pick up because my enemies never get close enough for me to use them.