This hadith is narrated (from 'A'isha) on the authority of Ibn Shihab with the same chain of transmitters (and the words are): Safiyyah bint Huyayy, the wife of Allah's Apostle ﷺ, entered the period of menses at the occasion of the Farewell Pilgrimage after she had performed Tawaf Ifada in the state of cleanliness;
the rest of the hadith is the same.

حَدَّثَنِي أَبُو الطَّاهِرِ، وَحَرْمَلَةُ بْنُ يَحْيَى، وَأَحْمَدُ بْنُ عِيسَى، قَالَ أَحْمَدُ حَدَّثَنَا وَقَالَ، الآخَرَانِ أَخْبَرَنَا ابْنُ وَهْبٍ، أَخْبَرَنِي يُونُسُ، عَنِ ابْنِ شِهَابٍ، بِهَذَا الإِسْنَادِ قَالَتْ طَمِثَتْ صَفِيَّةُ بِنْتُ حُيَىٍّ زَوْجُ النَّبِيِّ ﷺ فِي حَجَّةِ الْوَدَاعِ بَعْدَ مَا أَفَاضَتْ طَاهِرًا بِمِثْلِ حَدِيثِ اللَّيْثِ .