[The ruling on Ḥajj for a young woman in times like these]

Answer—and Allah is the Granter of success: If the crowding reaches a point where the young woman cannot perform ṭawāf and saʿy except by jostling with unrelated men, then what appears to me is that performing Ḥajj falls from her—though not its obligation—exactly as they said regarding a maḥram for a woman: if she does not find a maḥram, performing Ḥajj falls from her, though not its obligation.
The reason is that a young woman’s traveling without a maḥram is a sin the Prophet—May Allah bless him and his family and grant them peace—prohibited, and likewise her jostling with unrelated men is a sin.
Among the well-agreed principles is that leaving a duty is lighter than committing a prohibition, for disobedience is a corruption and obedience a benefit—and warding off harms is given priority, among people of sound reason, over procuring benefits.
That said: if a young woman cannot perform ṭawāf and saʿy except by jostling with men, she may perform ṭawāf from the second floor, and it suffices for her—because she is excused; the same applies to saʿy. Likewise, anyone who fears for himself due to the intensity of the crowd may perform ṭawāf and saʿy from above.
We say this for several reasons:
1. The ḥadīth: “When you are commanded to do something, do of it what you are able,” and the verse: “Allah does not burden a soul beyond its capacity.” [al-Baqarah:286]
2. “Do not throw yourselves, by your own hands, into destruction.” [al-Baqarah:195]
3. The sanctity of the House—from the soil to the Pleiades.
If it be said: It is obligatory to keep ṭawāf pressed to the House, due to His saying: “and let them circumambulate the Ancient House,” [al-Ḥajj: 22] and the preposition “bi-” indicates adhesion,
We say: Yes—and those we mentioned have adhered as closely as they are able. Allah does not burden a soul beyond its capacity. [al-Baqarah :286]
What we have stated is preferable to delaying Ḥajj or leaving it.
Yes, it may be said: The young woman or the weak person can delay ṭawāf and saʿy until the crowd thins—even if the Days of Tashrīq pass; delaying ṭawāf for an excuse is permissible. The proof is what came from the Messenger of Allah—May Allah bless him and his family and grant them peace—regarding one of his wives: “Are we being detained by her?” They said: “She has performed ṭawāf.” He said: “Then not [detained],” or as narrated.
But which is preferable for the excused person: to perform ṭawāf andsaʿy from the second floor, or to delay them?
By analogy, it is not permissible to delay an act of worship beyond its time when it is possible to perform it in a deficient manner; one may not delay the prayer beyond its time if one can perform it with earth (tayammum) or seated. Accordingly, performing ṭawāf from the second floor during the Days of Tashrīq is preferable to delaying it.
A third solution remains: Is deputizing another to perform ṭawāf and saʿy valid due to this excuse?
Answer: The scholars of the madhhab have permitted the excused person to appoint a proxy for stoning the pillars. By analogy with their view: if the excuse persists for the whole time of ṭawāf and one fears the time will end before he is able to perform it, then deputizing is permissible. However, the ḥadīth “Are we being detained by her?” indicates that the excused person delays ṭawāf until the excuse is removed—even if the Days of Tashrīq pass.
Yes: if the excused person has companions who will not wait for the removal of his excuse, then in that case he may deputize—for that is the utmost he can do; and Allah does not burden a soul beyond its capacity.
If it be said: Ṭawāf al-Ziyārah is the greatest pillar of Ḥajj, so deputizing in it is not valid except for a hopeless (incurable) excuse,
We say: The excused person has already performed iḥrām and the standing [at ʿArafah]; and in the ḥadīth: “Ḥajj is ʿArafah.”
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1