I think once they enter and there is an exigency (missing person and blood spatter) no warrant is needed.
True. If they found something in the context of a welfare check in which the nanny let them in to search, it's 100% fair game without a warrant.
But they would not need a warrant to search a victim's home during a welfare check anyhow, unless the perp also lived there. Because they aren't seeking evidence to be used to charge someone and the victim would not be a suspect.