Bathing within thirty days after the brit for the father of the child

If someone has a brit within the thirty days of mourning, is it permissible for the sandek and the father of the child to bathe within the thirty days of mourning?

They are permitted to bathe as usual in hot water with soap. They are allowed to wear Shabbat clothes, and according to Sephardic custom, they are allowed to eat at the brit, while according to Ashkenazic custom, eating is prohibited.

Beit Yosef, Yoreh De'ah, Siman 391: "And it is written in the responsa of the Mahari"l that the father of the child and the mohel are permitted [to enter the meal] because it is their festival, and it is also written in the Prans (Siman RM) that the Maharam, within thirty days of his father's death, was the father of the child and bathed, and it is further written (in the Prans there) that it is permitted to wear Shabbat clothes until after leaving the synagogue, which is considered a festival since wearing Shabbat clothes is allowed, which is a prohibition of thirty days like ironing, and the Tashbetz (Siman 525) also wrote that it is permitted for the father of the child and the mohel to eat there. And in the Darkei Moshe, it is written that only after thirty days is it permitted to eat, but within thirty days it is forbidden to eat, and in the Taz, S"K 3, it is ruled that only for his father and mother, but in mourning for other relatives, it is permitted to eat within thirty days. However, the opinion of our teacher, the Rav, is that one should not eat even for other relatives. And the Chochmat Adam wrote, Klal 165:1 "And nevertheless, the father of the child, even for his father, is permitted to bathe on the night before the brit after seven days since it is not by law that it is considered a festival for him." And therefore, although the Taz was stringent regarding his father and mother, it is only regarding eating, but bathing is permitted.