He's killing for a reason, and if we assume that Dumbledore isn't lost to morality(as he seems not to be), then he certainly believes that the reason justifies an innocent death. If you're paying that sort of price though, you've got a pretty serious obligation to ensure that you get what you're paying for - in this case, an end to the murder of your family and the families of your allies. If killing her nasty does a better job of that than killing her cleanly, then light up the BBQ. It's better than killing her for nothing.

Also, before I sound like too much of a psychopath, I should point out that I'm well aware of how slippery a slope this sort of argumentation is, and how incredibly careful you need to be in applying it. But war involves lots of death, and if you're paying in lives either way, you really should try to get the best price you can. It sucks, but it was the best choice open to Dumbledore in the situation, so I won't fault him for following that path.