I would like to suggest another explanation that answers the question of how Avraham was able to perform the bris on Yom Kippur according to the medrash that says that Shem did not perform the bris. The medrash says that Hashem sent His hand and helped Avraham cut. The halacha is that when two people do a melachah together they are not liable on Shabbos or Yom Tov. Therefore, since Avraham performed the bris together with Hashem he did not violate the laws of Yom Kippur.
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