Answered by Shaykh Faraz Rabbani
In Nur al-Idhah, it states the following points as being mustahabat of wudu:
-To recite respective dua’as while washing the limbs.
What supplications did the Prophet (sallAllah-u ‘alayhi wa sallam) recite while washing the limbs?
Walaikum assalam wa rahmatullah,
Any supplication or dhikr fulfills the recommendation of being in a state of remembrance of Allah during one’s wudu, such as the shahada (la ilaha illa Allah) or salat on the Prophet (Allah bless him and give him peace).
There are no soundly established du`as during wudu from the Prophet (Allah bless him and give him peace), though such supplications exist from the early Muslims and have been mentioned by the scholars. [Shurunbulali, Imdad al-Fattah; Ibn Abidin, Radd al-Muhtar]