Mahmoud Isma`il Shell, the editor of Hajj and `Umrah Counsels at IslamOnline.net, states the following:
There are some options before pilgrims to choose between concerning throwing the pebbles
1. A pilgrim may stone in two days instead of three. There is no scholarly difference over this point. In this regard there are two choices before pilgrims for leaving Mina for Makkah: they may leave Mina on Dhul-Hijjah 12 after throwing the pebbles on that day, which is called anafar al-asghar (the lesser departure). A pilgrim here is to leave Mina before the sunset of that day according to the majority of scholars. However, Imam Abu Hanifah said, “A pilgrim may stay until before the dawn time of the thirteenth day, for a new day begins after dawn time.” Hence, a pilgrim may depart Mina before the dawn time of the thirteenth day, yet he would then be doing something undesirable (according to the majority of scholars).
The second choice before pilgrims concerning leaving Mina is to depart it on Dhul-Hijjah 13. This choice is preferable to the first, for it was reported that the Prophet (peace and blessings be upon him) left Mina on Dhul-Hijjah 13. Allah Almighty says: (Then whoso hasteneth (his departure) by two days, it is no sin for him, and whoso delayeth, it is no sin for him; that is for him who wardeth off (evil). Be careful of your duty to Allah, and know that unto Him ye will be gathered) (Al-Baqarah 2:203).Read Also:
2. Pilgrims may throw the pebbles any time during all the days of throwing, i.e., from morning until the dawn of the following day. This is allowed for pilgrims so that they have plenty of time to perform this ritual at ease, especially if there is a valid excuse like heavy rain and the like. This viewpoint is reported to have been adopted by `Ata’, the eminent jurist of Makkah in his time, and by Tawis, the eminent jurist of Yemen in his time. Both scholars received knowledge at the hands of one of the most knowledgeable persons in the Muslim Ummah, Ibn `Abbas (may Allah be pleased with him). So was also the opinion of Abu Ja`far Al-Baqir, an eminent scholar, and some contemporary scholars from the Shafi`i, Maliki and Hanbali schools. This view was also reported to have been held by Imam Ahmad.
3. In a situation like that referred to in the question in hand, groups of pilgrims may entrust some persons to throw the pebbles on their behalf on the condition that the person entrusted with this task throws the pebbles for himself first. This applies also to the cases of pilgrims who for valid reasons such as illness, old age, pregnancy, etc., cannot throw the pebbles themselves.
4. A pilgrim may delay throwing all the pebbles until the last day of stoning. This is the point of view of the Hanbali and Shafi`i scholars. According to them, a pilgrim may throw all the pebbles, including those to be thrown on the `Eid Day, on Dhul-Hijjah 13, for the days of Mina are regarded as one extended time.
With respect to spending the nights of these days at Mina, the majority of scholars see that it is wajib (obligatory) and giving it up requires one to slaughter an animal as an expiation. But the Hanifi scholars and Ibn Hazm believe that it is only an act of Sunnah.
Regarding the same point, some scholars are of the opinion that pilgrims who have valid reasons, like illness or fearing for their safety or money or the like, may be exempted from spending these nights at Mina. This case applies also to the pilgrims in a situation like that referred to in the question in hand.