Praise be to Allah.
The Sunnah is to do wudu’ as for prayer for the deceased before ghusl, because of the hadith of Umm ‘Atiyyah (may Allah be pleased with her), who said: The Prophet (blessings and peace of Allah be upon him) said to them regarding ghusl for his daughter [who had died]: “Start on her right side and with the places of wudu’.” Narrated by al-Bukhari (1255) and Muslim (939).
An-Nawawi (may Allah have mercy on him) said: This indicates that it is recommended (mustahabb) to do wudu’ for the deceased. This is our view and the view of Malik and the majority. Abu Hanifah said that it is not recommended.
In our view, wudu’ should be done when starting to do ghusl, as in the case of one who is junub. End quote from Sharh Muslim.
But excluded from wudu’ in this case is rinsing out the mouth and nose; it is sufficient to wipe them with a wet cloth.
Ibn Qudamah (may Allah have mercy on him) said: No water should be put into his mouth or nostrils, according to the view of most of the scholars. This was stated by Sa‘id ibn Jubayr, an-Nakha‘i, ath-Thawri and Abu Hanifah. That is because if water is put into his mouth and nose, there is no guarantee that it will not reach his stomach, which is akin to mishandling of the body, and there is no guarantee that it will not come out onto his shrouds."(Al-Mughni 2/165).
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: That is because when the living person puts water in his mouth, he can swill it around and spit it out, but in the case of one who is deceased, if we pour water into his mouth, it may reach his stomach and cause some movement. We may say the same with regard to the issue of rinsing the nose; the deceased person cannot take water up into his nose and expel it, so in this case we say that water should not be put into his mouth or his nose."(Ash-Sharh al-Mumti‘ 5/131).
Shaykh Muhammad al-Mukhtar ash-Shinqiti (may Allah preserve him) said:
Based on that, instead of rinsing the mouth of the deceased or putting water in his nose, the water can be put on his lips; [the one who is washing him] can put two wet fingers on his lips, and also insert them into his nostrils. This is what was mentioned by the author (may Allah have mercy on him) when he said: He can put his two fingers that have been wetted with water between his lips, and wipe his teeth, and put [his fingers] into his nostrils and clean them, and not put water into his mouth or nose."(Sharh az-Zad).
And Allah knows best.