I do not think this person is wearing a wig, and I believe it is a woman. I believe this woman is a mother, and is in the 501st Legion. She has long, black hair.
I also do not think a man would go through the trouble of finding women's boots their size to take out the attack.
I would like to note that in nearly every unsolved case where the perpetrator is seen on video, with any type of concealment, always has speculation to the persons gender.
Missy Bevers with the full SWAT gear perp, the Florence Salon Murders with the Jeepers Creepers type outfit, Aliza Sherman's killer was fully concealed in a black getup, the person seen on footage in the Jennifer Keese case with the painting suit on but just happens to have their face concealed in the frame.
Notably, these unknown killers are speculated to be a man or a woman depending on the perception of who is watching the footage.
Also, most noteworthy to me, the victims where always women. I have yet to see a case with a murders concealed identity where a man was the victim and the perps gender was debated for male or female.