You can do it with an enchantment or an on hit event script on the weapon if you want it to still be enchantable.
To do it with an enchantment set magic effect conditions on the magic effect you link to the enchantment.
Thanks for the response. I was going to do an enchantment that can not be learned to keep my weapon unique, but if I can just write a script and put it on the weapon, that might be even better! You got my mind churning now.
So now I have new questions.

- Looking at the wiki (maybe a mistake, but... http://www.creationkit.com/Weapon_Script) I don't see an OnHit event for weapons. So what should my weapon script extend?
- Also, once I do get an OnHit event to fire, how do I get a reference to the actor I just clobbered?
Once I get there, I think I can figure out the rest.