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.
A Muslim who has a cut or the like in his face because of which he cannot wash the face during ablution nor can he wipe it during Tayammum, or cover it with a bandage and wipe over it, he can perform ablution and exclude the face, as stated by Muslim jurists, since the Prophet, sallallaahu ‘alayhi wa sallam, said: "When I order you to do something, do whatever you are able to do of it." [Al-Bukhari and Muslim]
Finally, it should be noted that the questioner should not undergo this operation without a serious necessity or need, particularly if it requires abandoning washing the face in ablution.
Allaah Knows best.