Even though it disturbs her, there is no provision in halacha for him to shave. Rather, he must gently explain to his wife that we must follow halacha even when it is difficult just as one would give up their job if it entailed working on Shabbos. However, there is a provision the opposite direction, a woman may shave her legs during the three weeks out of concern that she will become repulsive to her husband.
This only applies under normal marital circumstances. However, if there are problems, a Rav familiar with the details of the situation should be consulted.