Answer:
I say, and with God's success: It is proper etiquette to invoke Allah with the supplications narrated from the predecessors when washing each part during ablution, as these supplications, even if there is no hadith from the Prophet  regarding them, are acceptable as long as we do not attribute them to the Prophet , especially since they have been reported from the predecessors, and they fall under the general command to remember Allah, and there is no prohibition against them. The only authentic sayings from the Prophet regarding this are the two testimonies (shahadatayn) and the saying: "Glory be to You, O Allah, and praise be to You; there is no deity but You; I seek Your forgiveness and turn to You" after completing the ablution, while the rest are reported from the predecessors. Al-Tahawi said in his commentary on Maraqi al-Falah, p. 49: "Ibn Amir Hajj said: Our teacher, the guardian of his era, Shihab al-Din Ibn Hajar al-Asqalani, was asked about the hadiths mentioned in 'The Introduction of Abu al-Layth' regarding the supplications for the limbs, and he replied that they are weak, and the scholars are lenient in mentioning weak hadiths and acting upon them in matters of virtues, and nothing has been established from the Messenger of Allah , neither from his words nor from his actions. All of its chains are not free from suspicion of fabrication, and attributing these supplications to the righteous predecessors is more appropriate than attributing them to the Messenger of Allah ; out of caution against falling into the meaning of: "Whoever lies about me intentionally, let him take his seat in Hell." Regarding this, they said: as in 'Al-Taqrib' and 'Its Explanation': If you want to narrate a weak hadith without a chain, do not say, 'The Messenger of Allah  said,' or similar definitive phrases, but say: 'It was narrated from him such and such,' or 'It reached us,' or 'It was reported,' or 'It came,' or 'It was transmitted,' and similar phrases of uncertainty, as it is inappropriate to use definitive phrases for the weak hadith. Al-Hindi and others said: And nothing has been established from him except the two testimonies after completing it." Al-Kinani said in 'Tanzih al-Sharia', 2/70: "And he said in 'Al-Minhaj': I omitted the supplication for the limbs as there is no basis for it, and Al-Asnawi refuted him by saying: Not so, rather it has been narrated from various chains, including from Anas ." And Al-Nawawi said in 'Al-Adhkar', p. 29: "As for the supplication for the limbs of ablution, there is nothing reported about the Prophet صلى الله عليه وسلم, and the jurists have said: It is recommended to use supplications that have come from the predecessors, and they have added and omitted in them." Among these supplications: At the time of rinsing the mouth: "O Allah, help me in reciting the Quran, remembering You, thanking You, and worshiping You well." At the time of sniffing water: "O Allah, grant me the fragrance of Paradise, and do not let me smell the fragrance of Hell." At the time of washing the face: "O Allah, make my face white on the Day when faces will be white and faces will be black." At the time of washing the right hand: "O Allah, grant me my book in my right hand, and make my reckoning easy." At the time of washing the left hand: "O Allah, do not grant me my book in my left hand, nor from behind my back." At the time of wiping the head: "O Allah, shade me under Your Throne on the Day when there is no shade except Your shade." At the time of wiping the ears: "O Allah, make me among those who listen to the word and follow the best of it." At the time of wiping the neck: "O Allah, free my neck from the Fire." At the time of washing the right foot: "O Allah, make my feet firm on the Sirat on the Day when the feet slip." At the time of washing the left foot: "O Allah, make my sins forgiven, my efforts accepted, and my trade not to fail." And to mention the name of Allah, the Glorified and Exalted, when washing each part, and to send blessings upon the Prophet  after washing each part. And to say after completing the ablution: "I bear witness that there is no deity but Allah and that Muhammad is His servant and Messenger." And to also say after completing the ablution: "Glory be to You, O Allah, and praise be to You; there is no deity but You; I seek Your forgiveness and turn to You." Refer to: 'Tajdid al-Haqaiq' 1: 6-7, 'Majma al-Anhar' 1: 16, 'Bada'i al-Sana'i' 1: 23-24, and 'Al-Talimat al-Mardiya' on 'Al-Hadiya al-Ala'iya' p. 25, and Allah knows best.