The one sacrificing must be one of them. In her case, the money she is giving is a contribution and a gift to her husband. Therefore, it is her husband who is giving the sacrifice and not her. She doesn’t have to refrain from these things.

Can a wife give some money for buying the sacrificial animal to her husband? (For example, if the animal costs 500sr; she gives 200sr and her husband pays the rest). Does she also have to refrain from cutting nails and hair?