I think it’s possible that Brandon was playing with the assumptions we would make and that Vivenna isn’t actually hunting Vasher.
In OB chapter 108, she says that she’s hunting a sword (and gives enough description that it’s Nightblood) and the person who brought it to Roshar. In chapter 110, she asks our Rorsharan protagonists to warn Vasher she’s looking for him.
She was following the honorspren because they had noted Nightblood passing through. If she thought that Vasher was the last person to have him, then wouldn’t it have made more sense for her to prioritize finding Vasher over an obscure trail for Nightblood?
This is a large jump, but the next question is if she’s not hunting Vasher then who? I’d really like the irony if she was hunting Nale under valid laws.