May one celebrate an Upsherenish during Chol Hamoed?

Chol Hamoed Sukkos:[1] If the child was born on Chol Hamoed Sukkos, it is permitted to hold the Upsherinish on that day, on Chol Hamoed, [and so is the Sephardic custom[2]].[3] [In fact, some Poskim[4] rule that even if the child was born before Yom Tov, one may even initially delay the Upsherinish until Chol Hamoed in order to increase the joy and festivity and doing so is even a Mitzvah. However, the Rebbe negated any delay, as brought above in Halacha 2.] Nonetheless, despite the above letter of allowance, many are accustomed to delay the haircut until after Chol Hamoed.[5] [There is no definite Chabad  custom in this matter, and Rabbanim of Anash differ in their ruling on the matter.[6] Certainly, one who chooses to have it on the day of the birthday which falls on Chol Hamoed has upon whom to rely.]

Chol Hamoed Pesach:[7]  If the child was born on Chol Hamoed Pesach, the haircut is to be delayed until Lag Baomer.

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[1] See Nitei Gavriel 10:6; Shevach Habris 2:3

[2] Sefer Bein Pesach Lishavuos 19:11

[3] Michaber 531:6 that one may give a haircut to a child on Chol Hamoed [However, see M”A 531:8; Elya Raba 531:6; M”B 531:15 that this allowance only applies if the hair of the child is disturbing him]; Ginas Veradim Gan Hamelech 62; Devar Moshe 1:45; Nechpa Bakesef 2:7; Mizbeiach Adama p. 7; Shulchan Gavoa 531:13; Beir Heiytiv 531; Shaareiy Teshuvah 531:7; Kaf Hachaim 531:30; Implication of Igros Kodesh 8:289; Shevach Habris 2:3 that so he heard from Rav Groner and ruled Rav Dworkin

The reason: As there is no obligation to give a child a haircut prior to the Moed, as he is not Bar Mitzvah. [M”A 531:8; Taz 531:6]

[4] Ginas Veradim Gan Hamelech 62; Devar Moshe 1:45; Nechpa Bakesef 2:7; Mizbeiach Adama p. 7; Shulchan Gavoa 531:13; Beir Heiytiv 531; Shaareiy Teshuvah 531:7; Kaf Hachaim 531:30

[5] Rav Yekusiel Farkash that he has not seen anyone do so on Chol HaMoed, not amongst Anash, or other sects

[6] See Igros Kodesh 8:289 and 9:4; Shevach Habris 2:3 footnote 3 in name of Rav Groner that the Rebbe would instruct children who were born on Chol Hamoed to have their haircut take place then, on Chol Hamoed. And in name of a member of Anash who says that Rav Z.S. Dworkin ruled to him similarly to have a haircut take place on Chol Hamoed Sukkos; Likewise, Rav Yeruslavski has ruled to cut the hair during Chol Hamoed; However, Rav Farkash states that he has not seen anyone do so on Chol HaMoed, not amongst Anash, or other sects, and since this is the custom, it should therefore be respcted.

[7] See Igros Kodesh 8:289; 9:4; Shevach Habris 2:4 footnote 4 that so is Minhag Anash