Aliyah to the Torah for a Kohen during the days of mourning on Shabbat when there is no other Kohen

A Kohen in mourning is present in the synagogue on Shabbat, and there is no other Kohen besides him. Should he be called up to the Torah during the Torah reading on Shabbat?

If he is in the synagogue where he prays every Shabbat and usually receives the Kohen aliyah, he should be called up as a Kohen. However, if he is not usually called up for the Kohen aliyah, he should step outside when they call up an Israelite in his place.

Responsa Chatam Sofer, Part 2 (Yoreh De'ah), Siman 352: "Nevertheless, it is clear that in a place where a Kohen usually leaves the synagogue to call an Israelite in his place, even when he is in mourning, it is not considered public mourning if he leaves the synagogue. Nevertheless, if he does not leave and is called, there is nothing wrong with that." In Responsa Tashbetz, Part 2, Siman 276: "If it is Shabbat, he reads the Torah. Although on Shabbat he conducts himself in mourning privately, publicly it is forbidden to conduct oneself in mourning, and if he did not read the Torah and there was no other Kohen but him, it would be public mourning. If he leaves the synagogue after he has come there, it is even more public." In Mishnah Berurah, Siman 135, S"K 45, it is written: "A Kohen who is in mourning and there is no other Kohen in the synagogue on Shabbat, it is permitted to call him as a Kohen so that it does not appear as public mourning. On weekdays, he should not be called up because mourning is forbidden in Torah study. Nevertheless, both on weekdays and Shabbat, it is better that he first leaves the synagogue, and they call an Israelite and a Levite in place of the Kohen." In practice, if his leaving the synagogue is unusual, and he always receives the Kohen aliyah, it seems that even the Mishnah Berurah would agree that he should not leave, as the act of leaving itself is public mourning. However, if he often does not receive the Kohen aliyah, such as when he is not in the synagogue or leaves before the Torah reading, etc., it is not public mourning, and he may leave.