All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If a man performs Hajj or ‘Umrah on behalf of a woman, then he should perform the rituals as he performs them for himself, with the difference that he makes the intention for conducting the rituals on behalf of the person who has authorized him to perform Hajj on his behalf. So he should shave and cut his hair and perform such Sunnah acts that are required of men, and not women, such as Ramal (walking in an active gait) and Idhtiba‘. The same holds true for a woman who performs Hajj on behalf of a man. She should conduct the rituals just as she performs them for herself. She is not allowed to cut her hair, but she should only shorten her hair to the equivalent of a fingertip or so. Also, it is not permissible for her to do Idhtiba‘ or Ramal.
Allaah Knows best.