Everything I've seen usually says not to use wool. It may feel soft to you, but chemo makes the skin very sensitive and scalps would tend to be more so because they are usually covered with hair and not sensitized. Something with a little wool might be okay, but give it a good feel first.
Cotton or cotton blends and very soft acrylics like CSS seem to be best. She'll be indoors so warmth isn't quite the issue with someone outdoors in winter.
I'm sorry to hear about your MIL. I hope she does well on the chemo and doesn't feel too ill.