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)
- 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)