Ok, here is the exact wording of Killing Blow.
Killing Blow
If a model with the Killing Blow special rule rolls a 6 to wound in close combat, he automatically slays his opponent - regardless of the number of wounds on the victims profile. Armor saves and regeneration saves cannot be taken against a Killing Blow. A ward save can be attempted- if passed, the ward save prevents all damage from the Killing Blow.
Killing Blow is only effective against infantry, cavalry, and warbeasts... yadda yadda Heroic Killing blow...
So going by the wording, both the ignoring armor/regen AND the automatically slaying part only apply if the victim is of the appropriate unit type. Otherwise there is no effect.
If the caveat regarding infantry, cavalry, and warbeasts was appended directly after the "automatically slays his opponent" part, then that part would be the only conditional part of the rule and the ignoring armor/regen saves part would be always on regardless of the target.
But it is not, and so to get either part of the rule the target has to be an eligible unit type. So you can only ignore the armor save on a Stank if you have HKB, in which case you'll also instantly kill it on a 6 as well.