Praise be to Allah.
If the pilgrim who is doing tamattu‘ [‘umrah followed by Hajj, exiting ihram in between] is not able to do ‘umrah before Hajj, then he should change his intention from tamattu‘ to qiraan. So he should intend to do qiraan, i.e., doing Hajj and ‘umrah together.
Ibn Qudaamah (may Allah have mercy on him) said: If a woman who is doing tamattu‘ gets her menses before doing tawaaf for ‘umrah, and she is afraid of missing Hajj, or someone else fears missing Hajj [for another reason], he should enter ihram for Hajj with ‘umrah, and therefore will do qiraan, because of the hadith of ‘Aa’ishah, and because it is permissible to join Hajj with ‘umrah with no excuse, therefore it is more appropriate that it should be permissible to do that when there is the fear of missing Hajj.
End quote from al-Kaafi fi Fiqh al-Imam Ahmad (1/483)
This has been discussed previously in the answer to question no. 109336
In that regard there is no difference between the pilgrim doing tamattu‘ who has a sacrificial animal with him and the one who does not have a sacrificial animal with him, because he is only doing that to make sure that he will not miss Hajj, and this is something that may be applicable to both the one who has brought a sacrificial animal with him and the one who has not brought one with him.
Ibn Qudaamah (may Allah have mercy on him) said:
If the one who is doing tamattu‘ fears that he may miss Hajj, he should change the intention of ihram to Hajj, and thus he will be doing qiraan. The same applies to the one who is doing tamattu‘ and has the sacrificial animal with him; he should not exit ihram after doing ‘umrah; rather he should change the intention of his ihram to include Hajj along with ‘umrah, and thus he will be doing qiraan.
End quote from al-Mughni (3/422).
If he is now doing qiraan after he started out doing tamattu‘, the actions of ‘umrah will be included with his Hajj.
It says in Kashshaaf al-Qinaa‘ ‘an Matn al-Iqnaa‘ (2/416):
‘Umrah is waived in his case, i.e., he can combine its actions with the actions of Hajj, like all others who are doing qiraan, and that will count for the obligatory ‘umrah. End quote.
This is according to the view that it is possible to do tamattu‘ and bring a sacrificial animal. Otherwise there are some scholars who do not allow tamattu‘ for the one who has brought a sacrificial animal.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The correct view is that if a person has brought a sacrificial animal with him, he is not allowed to do tamattu‘, because the Prophet (blessings and peace of Allah be upon him) said: “If I had known before what I know now, I would not have brought the sacrificial animal and I would have exited ihram with you [following ‘umrah, then I would enter ihram again for Hajj].” Based on that, the one who has brought the sacrificial animal with him has no choice but to do either qiraan [‘umrah followed by Hajj without exiting ihram in between] or ifraad [Hajj on its own]. And if we say that if he has a sacrificial animal with him, he should not exit ihram but he may be doing tamattu‘, that would be a fourth type of Hajj that is not mentioned in the Sunnah, which is doing tamattu‘ without exiting ihram between ‘umrah and Hajj. This is something unprecedented.
End quote from ash-Sharh al-Mumti‘ (7/278)
With regard to your question about whether ‘Aa’ishah (may Allah be pleased with her) offered a sacrifice after she switched to doing qiraan?
The answer is that the Messenger of Allah (blessings and peace of Allah be upon him) sacrificed a cow on her behalf. In Saheeh Muslim (1319) it is narrated that Jaabir (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) sacrificed a cow on behalf of ‘Aa’ishah on the Day of Sacrifice.
With regard to the words of ‘Aa’ishah (may Allah be pleased with her), as narrated in Saheeh Muslim (1211): Allah enabled us to complete our Hajj and our ‘Umrah. And there was no sacrifice, charity or fasting required because of that, The scholars have answered that:
It was said that these words have been inserted (by a later narrator) and are not the words of ‘Aa’ishah (may Allah be pleased with her).
Ibn al-Qayyim (may Allah have mercy on him) said: This additional material – namely the words “And there was no sacrifice…” – have been inserted into the hadith and are the words of Hishaam ibn ‘Urwah, as was stated by Muslim in as-Saheeh.
End quote from Tahdheeb as-Sunan (1/190)
These words, which appear to be problematic, are not really problematic because they were narrated by Wakee‘ in a mawqoof report the isnaad of which ended with Hishaam ibn ‘Urwah and his father. He said: ‘Urwah said: Allah enabled her to complete her Hajj and ‘umrah. Hishaam said: And there was no sacrifice, charity or fasting required because of that. As that is the case, this additional material is separate from the rest of the text, because ‘Urwah and Hishaam are stating in these words that no report reached them concerning that. In other words, they are saying that they have no knowledge of that. But that does not necessarily mean that nothing of that nature happened. Perhaps the Prophet (blessings and peace of Allah be upon him) offered a sacrifice on her behalf, but news of that did not reach them. This interpretation may be applied, on the assumption that these were the words of ‘Aa’ishah. This is supported by the words of Jaabir, who said that the Prophet (blessings and peace of Allah be upon him) sacrificed a cow on behalf of ‘Aa’ishah.
It may be that what is meant by her words “And there was no sacrifice, charity or fasting required because of that” is that he did not instruct her to do any of those things, because he intended to do that on her behalf, as he did, according to the reports narrated by Jaabir and others.
End quote from al-Mufhim lima ushkala min Talkhees Kitaab Muslim (10/62)
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: Ibn Khuzaymah said: What is meant by the words “And there was no sacrifice, charity or fasting required because of that” is with regard to her not doing the first ‘umrah and making it up by doing it with Hajj, and not her ‘umrah that she did from at-Tan‘eem. This is a good interpretation.
End quote from Fath al-Baari (3/610)
An-Nawawi (may Allah have mercy on him) said: This interpretation is based on the assumption that she was speaking about herself, i.e., that there was no sacrifice, charity or fasting required because of that. But it is problematic if she was doing qiraan, because the one who does qiraan must offer a sacrifice, as must the one who does tamattu‘. It may be that this should be interpreted as meaning: I did not have to offer a compensatory sacrifice for committing any of the actions that are prohibited whilst in ihram, such as wearing perfume, covering the face, killing game, removing hair, clipping the nails, and so on. In other words, I did not commit any of the prohibited acts because of which I would have to offer a sacrifice or give charity or fast. This is the favoured view concerning the interpretation of this matter.
End quote from Sharh Muslim (8/145)
And Allah knows best.