Its kind of impossible to do. While you don't have to kill that many things at all, it would still be incredibly hard not to. I believe that there are only two people you must kill in Fallout 2, and have no idea about Fallout.
So what you are saying here is go through the whole game and not shoot, stab, blow up or disintegrate anything? Not even random encounters?
That would mean leaving Metzger, the Rat God, the raiders in Vault 15 and many more *bad* guys alive... that would be just as bad as shooting a kid in the groin with a plasma riffle... and totaly dull.
Yes, you can finish Fallout 1 without attacking anything or anyone. I've done it.
It's impossible in Fallout 2 because you have to kill Frank Horrigan, one way or another.