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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Principally the two hands are to be used in washing the face in the Wudhoo’. This was the practice of the Prophet, sallallaahu ‘alayhi wa sallam, and it is better to make one’s Wudhoo’ perfect. Nevertheless, it is permissible to use one hand to wash the face whether it is the right or the left one as long as the face is washed properly and completely through washing it with two or three handfuls of water. Al-Haafith Ibn Hajar, may Allaah have mercy upon him, said:
"It is evidence that it is permissible to rinse the mouse and sniff water up into the nose with only a handful of water. It also proves that the face has to be washed with the two hands when one uses only one handful of water since one hand can not wash the whole face in this case."
Al-Haafith, may Allaah have mercy upon him, means that in case of taking two or three handfuls of water it is sufficient to use one hand since it fulfils the command of washing the face completely.
Allaah Knows best.