Is a Shafi'i's prayer invalid if he does not renew his ablution after shaking a woman's hand, while a Hanafi's prayer is valid in the same situation?

Scholars have differed regarding the invalidation of ablution by touching a wife or a foreign woman. The preponderant opinion is that it does not invalidate ablution at all, unless something is emitted. As for shaking hands with unmarriageable kin (mahram), such as one's mother or daughter, it does not invalidate ablution by consensus.