What is the ruling on shaking hands with socks on for a man who studies at a mixed-gender university, and what is the ruling on shaking hands with elderly men?

I have previously answered concerning the ruling on a woman shaking hands with a non-mahram man. Here, it is added that some scholars have exempted from the prohibition the permissibility of shaking hands with an elderly woman who is not desired, and similarly an elderly man, provided that there is no fear of temptation from either side. If the elderly woman is not desired, then there is no harm in shaking her hand or touching her hand due to the absence of fear of temptation. Likewise, if the man is an elder who feels secure for himself and for her. However, if there is fear of temptation, then it is not permissible. Therefore, if temptation is absent between the two parties, it is permissible for a woman to shake hands with an elderly non-mahram man; otherwise, it is not permissible.