There is a conflict between two rulings regarding this matter:
1.
The command to shave the pubic hair and not leave it for more than forty days
Imam Muslim (258) narrated that Anas ibn Malik said: A time limit was set for us for trimming the moustache, cutting the nails, plucking the armpit hairs and shaving the pubes: that was not to be left for more than forty days.
An-Nawawi (may Allah have mercy on him) said: “A time limit was set for us” is like a Sahabi saying “we were instructed to do such and such” or “we were forbidden to do such and such”; it is to be attributed to the Prophet (blessings and peace of Allah be upon him), as if he said “the Messenger of Allah (blessings and peace of Allah be upon him) said to us…”, according to the correct view, which is that of the majority of hadith scholars and jurists.
End quote from Al-Majmu`, 1/286-287.
The ruling on not shaving the pubic hair for more than forty days is a matter concerning which the scholars differed.
The Hanafis are of the view that it is disliked to the degree that it is almost prohibited.
It says in Hashiyat Ibn `Abidin, 9/583:
The words “it is disliked to leave it” mean it is almost prohibited, because the Prophet (blessings and peace of Allah be upon him) said: “There is no excuse after forty days and (the one who does that) is deserving of punishment.” End quote.
The majority of scholars are of the view that it is disliked but not prohibited.
Al-Mirdawi (may Allah have mercy on him) said:
He should not leave it for more than forty days, as stated, and if he does that, it is disliked. This was stated clearly in Al-Mustaw`ab, An-Nazm and elsewhere.
End quote from Al-Insaf, 1/255.
An-Nawawi (may Allah have mercy on him) said:
Cutting the nails; removing pubic hair by shaving, plucking, cutting, using a depilatory paste or otherwise, although shaving is best; and it is recommended to remove armpit hair using one of these methods, although plucking is better for the one who is able to do it. And it is recommended to trim the moustache so that the edge of the lip can be clearly seen. And in all these matters, one should start on the right and not delay it when it is needed. It is emphatically disliked to delay it for more than forty days, because of the hadith in Sahih Muslim which forbids doing that.
End quote from Rawdat at-Talibin, 3/234.
2.
Prohibition on the one who wants to offer a sacrifice removing any hair from his body during the first ten days of Dhul Hijjah, until he has offered his sacrifice.
Imam Muslim (1977) narrated from Umm Salamah that the Prophet (blessings and peace of Allah be upon him) said: “When the ten (days of Dhul-Hijjah) begin, and one of you wants to offer a sacrifice, let him not remove anything from the hair of his head or his body hair.”
The scholars differed concerning the ruling on the one who wants to offer a sacrifice shaving any of his hair during these days. Some of them said it is permissible, some said it is disliked and some said it is prohibited.
Ibn Qudamah (may Allah have mercy on him) said:
He said: “Whoever wants to offer a sacrifice, when the first ten days begin, should not remove anything from his hair or skin.” The apparent meaning of this hadith is that it is prohibited to cut one’s hair; this is the view of some of our companions, and Ibn al-Mundhir narrated it from Ahmad, Is-haq and Sa`id ibn al-Musayyab.
Al-Qadi and some of our companions said: It is disliked, not prohibited. This was also the view of Malik and ash-Shafa`i…
Abu Hanifah said: That is not disliked, because it is not prohibited for him to be intimate with his wife or wear regular clothing, so it is not disliked for him to shave his hair and cut his nails, like one who did not intend to offer a sacrifice.
And there is a hadith narrated by Umm Salamah from the Messenger of Allah (blessings and peace of Allah be upon him), according to which he said: “When the first ten days begin, if one of you wants to offer a sacrifice, let him not remove anything from his hair or his nails, until he offers his sacrifice.” Narrated by Muslim. What is implied by him telling them not to do that is that it is prohibited. End quote from Al-Mughni, 13/362.
An-Nawawi (may Allah have mercy on him) said:
Our view is that removing anything of the hair or nails during the first ten days, for the one who wants to offer a sacrifice, is disliked in the sense that it is not appropriate, until he offers his sacrifice.
Malik and Abu Hanifah said: It is not disliked.
Sa`id ibn al-Musayyab, Rabi`ah, Ahmad, Is-haq and Dawud said: It is prohibited.
And it was narrated from Malik that he regarded it as disliked…
End quote from Al-Majmu` Sharh al-Muhadhdhab, 8/329.
Based on that:
This issue is subject to different opinions, and we have not come across any answer from any of the scholars for your particular question. What appears to be the case – and Allah knows best – is that if someone forgets to shave his pubic hair, and delays it until after the first ten days, that will increase the period to more than forty days, so he should shave his pubic hair. Moreover, it is not prohibited for the one who wants to offer a sacrifice to shave any of his hair, according to the majority of scholars. As for the view that it is disliked, the ruling that it is disliked does not apply in the case of need, and the need to shave the pubic hair, as mentioned in the question, is a valid need.
And Allah knows best.