Is it obligatory for a woman to insert her hand into her vagina when performing ghusl to remove remnants of a man's fluid?

When performing ghusl (ritual bath) after major ritual impurity (janabah), a previously married woman (thayyib) must ensure water reaches the visible parts of her vulva when she squats to relieve herself, because these parts are considered external. However, washing the inner part of the vagina is not obligatory. Al-Nawawi reported that Al-Shafi‘i and the majority of his companions explicitly stated this. He also mentioned that Imam al-Haramayn said it is not obligatory to get water beyond the meeting point of the labia.