The Messenger of Allah ﷺ never touched a woman with his hand. He would only take a vow from her and when he had taken the (verbal) vow, he would say: You may go. I have accepted your fealty.
مَا مَسَّ رَسُولُ اللَّهِ ﷺ بِيَدِهِ امْرَأَةً قَطُّ إِلاَّ أَنْ يَأْخُذَ عَلَيْهَا فَإِذَا أَخَذَ عَلَيْهَا فَأَعْطَتْهُ قَالَ اذْهَبِي فَقَدْ بَايَعْتُكِ
The Messenger of Allah ﷺ never touched the hand of woman, but he received the oath of allegiance from her. When he received the oath of allegiance from her, she gave it to him, and he said: Go, I have received your oath of allegiance.
عَنْ بَيْعَةِ رَسُولِ اللَّهِ ﷺ النِّسَاءَ قَالَتْ مَا مَسَّ رَسُولُ اللَّهِ ﷺ يَدَ امْرَأَةٍ قَطُّ إِلاَّ أَنْ يَأْخُذَ عَلَيْهَا فَإِذَا أَخَذَ عَلَيْهَا فَأَعْطَتْهُ قَالَ اذْهَبِي فَقَدْ بَايَعْتُكِ
The Messenger of Allah ﷺ never touched the hand of woman, but he received the oath of allegiance from her. When he received the oath of allegiance from her, she gave it to him, and he said: Go, I have received your oath of allegiance. (Using translation from Abū Dāʾūd 2941)
عَنْ بَيْعَةِ النِّسَاءِ مَا مَسَّ رَسُولُ اللهِ ﷺ بِيَدِهِ يَدَ امْرَأَةٍ قَطُّ إِلَّا أَنْ يَأْخُذَ عَلَيْهَا فَإِذَا أَخَذَ عَلَيْهَا فَأَعْطَتْهُ قَالَ اذْهَبِي فَقَدْ بَايَعْتُكِ