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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is absolutely no doubt that it is more appropriate to hire a religiously committed and good Muslim teacher. That is because he is most likely to give the children of Muslims good education and sound direction while we cannot guarantee that the non-Muslim would not corrupt them.
However, if there is no Muslim teacher, then there is no harm to hire a non-Muslim to teach the mentioned subjects. Also, we have to investigate well who could be entrusted with that job.
In principle, there is no harm to hire non-Muslims because the Prophet, sallallaahu ‘alayhi wa sallam, hired ‘Abdullaah ibn Urayqit, who was a non-Muslim, as a guide in his migration to Madeenah. ‘Aa’ishah narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and Abu Bakr hired a man from the tribe of Bani Ad-Deel as an expert guide although he was a follower of the religion of the pagans of Quraysh. The Prophet, sallallaahu ‘alayhi wa sallam, and Abu Bakr trusted him and gave him their two riding camels. [Al-Bukhari]
In any case, you should do your best to find a Muslim teacher. For more benefit, please refer to Fatwa 81846.
Allaah Knows best.