Doctor Hissam ddin ibn Musa Hifanuhu, the clerk of Jurisprudence and its Principles at Al Quds mosque said:
The fundamental of hajj is that all its rituals should be performed by the pilgrim himself. Nonetheless, it’s allowed by scholars to entrust someone with throwing pebbles and slaughtering sacrificial animals.
Pertaining to pebbles throwing, it is permissible in sharia law to entrust someone in the case of sickness, pregnancy, old age and (women with) weaknesses when there is a lot of traffic and she’s scared for herself. Then it is permissible for her to entrust someone to throw the pebbles, and it is obligatory for the representative to throw on behalf of himself first then on behalf of the person he represents.
But for slaughtering the sacrificial animal, one can absolutely entrust anyone, be it with reason or without any reason, even though it’s better for the person performing hajj to take care of slaughtering the sacrificial animal himself based on prophet Mohammad’s doing as it is seen in the authentic hadith: ‘the prophet slaughtered sixty three camels and then handed the remaining to Alli’ as imam Muslim narrated.
And for the remaining part of hajj rituals, it is not permissible to delegate someone else, such as tawaaf, walking sa’y , standing at Arafat, staying at Musdalifa and Mina. These parts and duties must be done in person, but if one is sick then no problem for such person to be carried in tawaf and sa’y. He can also ride (usually on stretchers) to Arafat and mina. It is permissible for a sick and healthy person to sit in Arafat.