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.
We have not come across what suggests that this supplication is attributed to the Prophet but it is acceptable to supplicate with it. However, your saying "Wa laa tadhurrahum" literally means, "and do not harm them," which is an inappropriate expression as this is attributing harm by itself to Allaah while He both harms and benefits. If you say, "Wa 'aafihim (Keep them safe)," or "Wa ihfathhum (protect them)," or "Isrif 'anhum as-soo' (keep evil away from them)," then this would be more appropriate. Ibraaheem (Abraham) said: {And it is He Who feeds me and gives me drink. And when I am ill, it is He Who cures me, and Who will cause me to die and then bring me to life, and Who I aspire that He will forgive me my sin on the Day of Recompense.} [Quran 26:78-82]
Prophet Ibraaheem did not say, "Who made me sick;" rather, he attributed sickness to himself as a way of having good manners with Allaah even though all matters are in the Hands of Allaah.
Also, ‘Ali ibn Abi Taalib narrated that when the Prophet stood for the prayer, he used to say, “I turn my face in complete devotion to the One Who is the Originator of the heavens and the earth, and I am not of the polytheists. Verily my prayer, my sacrifice, my living and my dying are for Allaah, the Lord of the worlds; there is no partner with Him … Here I am at Your Service and Grace, and the whole of good is in Your hands, and evil is not attributed to You.”
So, it is part of good etiquette that evil is not attributed to Allaah.
Allaah knows best.