Undead substitute their Charisma for their Con in many things, so this makes sense.
Charisma is your strength of self, your confidence and your belief in yourself, essentially. By the book's inference, Undead use their belief in themselves to bolster their existence in this world. "I am, therefore I am." sorta. By turning a Constitution Drain into a Charisma drain against the Undead, you essentially dispel that self-confidence, and thus, achieve the same goal.
I support the Charisma Drain idea. Plan. Thing.