For the validity of wudu' you need to have done at least the fard parts which are mentioned in (5:6):
you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful.
If you have done so your wudu' is valid your skin may get dry afterwards it doesn't even play a role unless you have interrupted your wudu' in that case some madhhabs hold the opinion that as long as your skin shows some wetness you may go ahead else you need to restart from zero.
As for the case of performing wudu' and shaving the beard or shedding even if this might be considered as sinful or even haram by scholars. There's consensus that this doesn't per se break or invaldidate a wudu' performed before (as long as there's no other reason for which wudu' broke), but some scholars discussed whether or not one should re-do the washing of the body part which was "shaved". Islamweb offers a fatwa #109587 on that in Arabaic quoting from a maliki book of fiqh the difference of opinion on the necessity of washing.