All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the husband of a woman or her father offers a sacrifice on her behalf (among the members of his household), then she is not obliged to refrain from removing (anything from) her hair or skin according to our view in Islamweb. The person who is required to refrain from that is the husband or the father. However, if it is herself who would offer the sacrifice, then she should not take anything from her hair or skin.
However, the forbiddance mentioned in the Hadeeth means dislikeability and not prohibition according to the view of the majority of the scholars .
Even the scholars who are of the view that this is prohibited, they permitted taking from the hair or skin for necessity.
Therefore, if such a woman is harmed by leaving the hair of her moustache to an extent that she cannot bear, then we hope that this is a necessity that makes it permissible for her to remove that hair. For more benefit, please refer to Fatwa 88747.
Allaah Knows best.