Aliyah to the Torah on Shabbat during the seven days of mourning when his wife gave birth

If a man's wife gave birth, and he is on Shabbat during the seven days of mourning, and the custom in the synagogue is to call up to the Torah on Shabbat someone whose child was born, should he receive an aliyah on Shabbat during the mourning?

He should not be called up to the Torah, and it is preferable for him to leave the synagogue and listen to the reading from outside.

The Taz wrote in Yoreh De'ah, Siman T, Sif Katan: "And the Rashal wrote in a response, Siman 71, that a mourner whose son's circumcision is on Shabbat should not be called up to the Torah, even though in some places it is customary that the father of the son is obligated to be called up on the day of his son's circumcision, nevertheless, it is not considered public." However, the Pri Chadash in Yoreh De'ah, Siman T, wrote: "The Taz wrote in the name of the Rashal that a mourner whose son's circumcision is on Shabbat should not be called up to the Torah. And even though it is customary that the father of the son is obligated to be called up, it is not considered public. But this is not for us, who are accustomed to make a row, and those who are called up make a 'Mi Sheberach' for the father of the son, there is no greater public display than this, and it is appropriate to call him up to the Torah." And in practice, the poskim decided that he should not be called up.