What happens if you don't kill Crispin?

I just completed the mission where you have to kill Crispin in order to

assume his identity for the auction.

Near the end of the mission, Clara says something along the lines of

"Maybe we had to kill Crispin, but at least we can save the girl" (Poppy)

I retried the mission many times attempting to beat it without killing Crispin, but I can't get close enough to him before he runs away.

So, is it possible to knock out Crispin, rather than killing him? Does it affect the storyline or the dialog at all?

Solution 1:

Well, I managed to knock out Crispin without killing him by using a Blackout and running past his guards.

Unfortunately, the dialog was exactly the same (Clara still says "Maybe we had to kill Crispin..."), so most likely the storyline is not affected at all. Oh well.

Solution 2:

You can't not kill Crispin, even if you knock him out it counts as him being killed (I played full stealth without shooting unless I really had to).
What Clara meant is maybe something good (saving the girl) can come out of this, even though you had to do something bad initially (killing Crispin)