The Answer;
In the name of Allah, Most Gracious, Most Merciful.
According to summary of two sayings of the beloved Prophet (saw), “The person who begins wudu by saying, “Bismillah”, his whole body from head to toe, is purified and the one who does not say, “Bismillah” before wudu, only purifies the washed portion of his body.” (Sunan Dār Quṭnī, pp. 108, 109, vol. 1, Ḥadīš 228, 229)
And Allah(swt) alone knows best.