How does a person who has had mouth or nose surgery perform ablution (wudu)?

The ruling on rinsing the mouth (mazmaza) and nose (istinshaq) during ablution is a matter of scholarly debate. This is due to the difference of opinion regarding whether the mouth and nose are considered part of the face, which must be washed in wudu. According to the majority of scholars, including the Hanafi, Shafi'i, and Maliki schools, rinsing the mouth and nose is a sunnah (recommended act) of ablution. (Marghinani, al-Hidaya, 1/16; Nawawi, al-Majmu‘, 1/465; Khattab, Mawahib, 1/245) In the Hanbali school, however, rinsing the mouth and nose is obligatory (fard) in both ablution and ritual bathing (ghusl). (Ibn Qudamah, al-Mughni, 1/88) The evidence of the majority is stronger and more accurate in this matter. Accordingly, since washing the mouth and nose is considered sunnah in ablution, omitting this step due to illness, surgery, or even without a reason does not invalidate the ablution.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu