In the Qur’an, Allah has placed the responsibility on the Muslim Ummah to convey the message of Islam to mankind. Referring to this, Allah Almighty says, (Thus We have appointed you a middle nation, that ye may be witnesses against mankind and that the Messenger may be a witness against you…) (Al-Baqarah 2: 143)
there is nothing wrong in donating the Qur’an to a non-Muslim library. Indeed, it is an excellent means of informing non-Muslims about the Qur’an and its noble teachings.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following: I consider it extremely important for us Muslims living in this part of the world, to use all resources and methods available to us to convey the message of Islam, and there is no better way of doing the same than exposing people to the Qur’an.

the Qur’an is the miracle of Allah to Muhammad (peace and blessings be upon him) and all those who are exposed to it, who have an open heart, would be guided to the message, Allah willing.
So, it is an excellent step on your part to provide such copies to the library and you don’t need to worry about the desecration. in sha’ Allah, Allah will preserve His Book intact, and He will reward you for your intention. Allah says in the Qur’an: (…Struggle with them a mighty struggle through the medium of the Qur’an.) (Al-Furqan 25: 52)