Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Yes, a woman may perform the Hajj Badal for a man and vice versa. However, it is best for someone who has already performed their own Hajj to perform the Hajj-e-Badal (of someone else). (Aap Ke Masa'il Aur Unka Hal Vol.4 Pg. 75)