Can a woman delegate someone to stone the Jamaraat on her behalf if she is afraid of the crowds?

If there is severe overcrowding in which there is fear for
women, it is not permissible for a woman to join that crowd, because that is
exhausting for her and because she is going to stone the Jamrah without
being able to focus on the action because of the severity of the crowding.
For example, if the people want to hasten on and depart after two days, and
they have to stone the Jamaraat when the sun reaches its zenith and then
depart, in this case it is not possible for the woman to stone the Jamaraat
all, because it is dangerous for her. So in this case we say: Delegate
someone (to stone the Jamaraat on your behalf), and there is nothing wrong
with that. But in other cases, such as on the eleventh day (of
Dhu’l-Hijaah), it is possible to delay the stoning from the meridian until
the time of ‘Asr or until the night, and even until dawn. So the matter is
broad in scope, praise be to Allah. 

Majmoo‘ Fataawa Ibn ‘Uthaymeen
(23/122). 

The scholars of the Standing Committee for Issuing Fatwas
were asked: Is it permissible to stone the Jamaraat during the day of Hajj
nowadays on behalf of women, because of the severe overcrowding? 

They replied:

Allah, may He be exalted, say (interpretation of the
meaning):

“Allaah intends for you ease, and He does not want to make
things difficult for you”

[al-Baqarah 2:185]

“Allah does not want to place you in difficulty”

[al-Maa’idah 5:6]. 

Hardship and difficulty are not the nature of this religion
by virtue of these two verses and similar texts. And women’s situations
vary: some may be pregnant and physically very large, or they may be
emaciated, or sick, or elderly, and some may be strong. In the case of a
woman who has one of the excuses referred to or something similar to that,
it is permissible to appoint someone (to stone the Jamaraat) on her behalf,
and there is no problem with that. The one who does the stoning on her
behalf should not do that until after getting her permission before he
(stones the Jamaraat) on her behalf. So he should throw stones on his own
behalf first, then on her behalf. As for the one who is strong, if the
hardship involved is extraordinary, it is permissible to appoint someone to
do the stoning on her behalf in the same manner as described above; he
should throw stones on her behalf after doing so on his own behalf. The
person who does the stoning on another person’s behalf should be a fellow
pilgrim.

And Allah is the source of strength. May Allah sent blessings
and peace upon our Prophet Muhammad and his family and companions. End
quote. 

Fataawa al-Lajnah al-Daa’imah,
11/283 

It also says (11/284): 

When it is very crowded, it is permissible for a woman to
appoint someone to stone the Jamaraat on her behalf, even if her Hajj is the
obligatory Hajj. That may be done if she is sick or weak, or so as to
protect her pregnancy if she is pregnant, and to protect her honour and
dignity, so that it will not be transgressed because of the severe
crowding. 

Standing Committee for Academic Research and Issuing Fatwas.