I tested the Bill Hook against chaos warriors using Riposte talent which guarantees a critical hit after a timed block.
Special pull attack, light attack, push attack and heavy attack did not kill the chaos warrior when hit in the head and other attacks could not be tested because the first one consumes the buff.
The same test with Rapier gives opposite results.
Perhaps the new weapon is missing something in the code that makes Killing Shot ignore it?
Problem seems to be that you tested on Chaos Warriors. Iirc, Killing Shot only works on “man-sized” enemies, which CWs are not. Try testing on Stormvermin or Maulers.