All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The majority of Muslim scholars believe that the expiation for breaking an oath should not be given to non-Muslims as is the case of other obligatory charities. The Hanafi scholars, however, hold a different opinion in this regard.
Al-Kaasaani said in his book Badaa’i' As-Sanaa'i', “It is permissible to offer the expiation for breaking oaths and vows and the like to the poor among the People of the Book, to the exclusion of Zakah, according to the view of Abu Haneefah and Muhammad .”
Abu Yoosuf said, “Permissibility is restricted to vows, voluntary charity, and Hady (sacrificial animals in Mut‘ah Hajj), apart from expiation. The logic of this opinion is that the expiation for breaking an oath is an obligation that is ordained by Allaah The Exalted; therefore, it should not be paid to non-Muslims, just like Zakah. However, vows can be paid to non-Muslims because it is the person who makes it obligatory on himself.”
Hence, it is impermissible to pay the expiation for breaking oaths to non-Muslims, according to the correct opinion of scholars.
Moreover, it is impermissible to give the expiation for breaking oaths to non-Muslim charitable societies as they may pay it in other than its lawful channels (paying it to other than its eligible recipients). However, there is no harm in paying the expiation for breaking oaths to Muslim charitable societies, if the person is certain that they would give it to its eligible recipients (the poor and needy among Muslims).
The fact that you live in a country where you cannot find needy Muslims does not justify paying the expiation to other than its eligible recipients. There are so many needy people in Muslim countries and it is easy for you to pay this money to reliable charitable organizations or even individuals to deliver it on your behalf.
Allaah Knows best.