How does the Destruction school fit into a "mage-assassin" build?

I'm playing a stealthy mage, and what I've found useful are the two enhancement perks to Frost and Shock spells, Deep Freeze and Disintegrate, particularly for the reason you identified: fixing problems after enemies detect you.

The biggest problem with Destruction is that all the spells are loud and flashy: they don't fit well with a perfect stealth scenario.

As James mentioned in the comments, you can use Illusion's Quiet Casting perk to mitigate the problem somewhat, but that requires a deep investment into Illusion and there's been some concern as to whether it's really effective: I personally didn't bother to invest in it.

So, barring that, it's almost a given someone will detect you: you might be okay against single targets, but in a group, or in broad daylight, you're going to have to deal with some amount of detection. The trick is to encapsulate the problem and avoid the people detecting you from alerting others.

With Deep Freeze, you can paralyze your opponent when its health is low, allowing you to finish them off. With Disintegrate, you can just completely destroy them once their health goes below 15%.

I haven't bothered with Impact, but it would have the same effect: stun the enemy long enough for you to do away with them before they can run.

For the same reasons, you want to avoid the enhancement perk to Fire spells, Intense Flames, which would cause your opponents to flee. Picking Master Destruction is probably not going to be worth it either, as Master-level Destruction spells are area-of-effect and not very stealthy.

In summary, if you're going to take Destruction, you'll probably want the following perks:

• Novice Destruction
• Apprentice Destruction
• Adept Destruction
• Expert Destruction (to get the mana savings on the most powerful single-target Destruction spells)
• Either:
  • Augmented Frost 1 and 2 and Deep Freeze, or
  • Augmented Shock 1 and 2 and Distintegrate
• Destruction Dual Casting (optional, to get Impact)
• Impact (optional)

Well...this is interesting. Illusion is the trick to this build. I never bothered with things such as the points, as every character you make should have enchanting. 100% reduction for destruction and illusion are for my build. I don't grab impact, but I will grab Ice and Shock spells. Fire just has too much wow factor, whereas an icicle from the corner proves effective. The tricks being for 100% illusion reduction is that destruction spells, even with the illusion quiet casting, will still cause some semblance of an uproar. Which is where the 100% illusion reduction comes in. The use of Invisibility in a frequent fashion will yield great stealth results with no alarming of an opponent (to detected state, though clearly they may have some concerns about getting shivved out of nowhere.) All in all, there's not a need for dual casting in a build like this. I found that this build is just interesting and effective, and I personally find it more fun than say...the x30 dagger damage and overkill bow type stealth builds, because there's not exactly a simple way to upgrade your magic damage without enchants. Course, you could put points in mana and not build for 100% reduction in both schools, instead upping your damage output for your destruction spells. It's totally up to you. Personally, I like my simple stuffs. Also...I think people need to recall that Necklace, Ring, Helm, Armor are the four pieces you can enchant to 25% reduction. I'd like to hear of more build ideas, but so far I liked this one utilizing Invisibility best. Though it's definitely something that requires finesse.

The mod, Spell Sneak Attacks makes all Destruction projectile spells benefit from sneak attack multipliers, and items that modify sneak attacks, like the Dark Brotherhood's Shrouded Gloves.

It also adds a new "Silent casting" enchantment as an alternative to the Illusion perk (so you won't need to have a high Illusion skill just to get Silent Casting).

Destruction and illusion together with sneak can make a very interesting combo. Lay down runes near exits, sneak to the middle of the room while invisable, charge a master spell while invisable, and release, the enemies are weakened, start throwing fear and fury spells around to create more chaos, fleeing enemies are killed by runes and their enraged allies, and you slip away into the shadows... Slit the last guy's throat and you're done.