Just got through the entire DB quest line without ever killing Narfi. (Personally, I would just as soon find whoever put the contract on Narfi and off them instead.)

Steps to avoid killing Narfi:

1) Join DB and get your first three contracts
2) Kill one of the contracts
3) Return to the sanctuary.
4) Arrange contract with Muiri
5) Return to the sanctuary and find out you are the Listener
6) Kill another one of the three initial contracts
7) Return to the sanctuary and begin the process of killing the intermediary targets on the way to the Emperor.

You never have to kill the third contract target of those initial three that Nazir gives you in order to get all the way to the end of Hail Sithis.