Personally, I'd leave it as is. Counting the fact that Shroud of Death circumvents anything based on Con. as is, it makes more sense to just leave it Cha.-based.

Interestingly, as long as you have a 14 or higher Charisma, you technically don't need to feed on blood to continue existing. You really only need to feed to fuel your powers. I like that, and how it plays into the whole 'kinda-sorta a vampire, but not really'.