I don't think she'd wearing a wig. When the girls shaved thier heads, they are rarely photographed with wigs. I don't think they ever wore any, except Tatiana in 1913. If I remember correctly, Tatiana even wrote in a letter after her head was shaved the second time that she was so happy she didn't have to wear a wig.
There are some pictures after thier heads were shaved with hats on, but you can tell there is nothing but their bare heads underneath.