Everyone will tell you to do the Assassin quests or Thief quests... of course you will... you're an assassin. Even if you ask how to be an assassin with no magic, you would be recommended to take Illusion or Conjuration.
My advice is this:
Bow
Damage perks only. Don't worry about stagger or paralyze perks, nor the Ranger or the one that gets your arrows back.
1 hand
(I dual daggers) Damage only. Daggers do less damage but are faster. So any enchant will proc more. And... it looks cool.
Block
if you want to... sometimes you need that torch to see. Bashing with the torch also does damage and fire damage. Don't take the block perks that prevent damage, take the bashing perks... they stagger your enemies. This helps when you have to melee those pesky dragons.
Sneak
All perks and max out, most will say ASAP, but I believe in learning as you go, so you appreciate the Shadow Warrior perk.
Magic
(Any type) Leave it at home... you don't need it.
Alchemy
Alchemy is your savoir (FYI, Alchemy is considered a thief skill in Skyrim). You can make potions and poisons to deal with any situation. Yes it takes work, but it is worth it.
Paralyze/damage, that's why you don't need it on bows... 15% chance for a few secs or 100% chance for 22 secs. There are not too many bosses you can't kill in 22 seconds while they are lying on the floor.
I use damage/magic drains on mages. You can make invis/health regen for the Oh Crap situations.
And Dragons, damage/heath dot... especially when you get to use each poison twice with the perk.
Smithing
To enhance your weapons and armor.
Enchant
I waited till level 40 and above for this. This is an awesome skill, but if you want to make a non-magic assassin I would opt against it. I am uber enough without it.
Armor
Take the armor type of your choice, but light armor has a regen stamina perk.
Regardless, take the time to get beat up so when you need protection, you armor skill is helping you to survive.
Now, do I win every fight? — No, but it is rare that I lose and only if I get surprised.
Can I one-hit Dragons? — I used to, until I downloaded Deadly Dragons, but yes.
Did I get my @$$ beat when I first started out? — Of course. Learning from the failures makes you succeed more often later on.
This is my opinion only, it is your game... play it the way you want.