The scalp is the anatomical area bordered by the human face at the front, and by the neck at the sides and back.
Yes, it is permissible for a woman to shave her scalp in the aforementioned situation.
And Allah knows best.
Applying any material on the skin or scalp is allowed even if it is Najis material as far as you clean the area before performing Wudhu or Salaah. Synthetic alcohol is not Najis according to many Maraaje'. Some scholars say that any intoxicant alcohol is Najis. Nevertheless, whether it is Najis or not Najis, it is allowed to apply it on the body or scalp.