Is it permissible to shake hands with women aged thirty, forty, and above, or to speak with them, knowing that I do not desire them, by analogy with the permissibility of shaking hands with an old woman who is neither desired nor desires?

Shaking hands with an old woman who is not desired is permissible. However, a woman in her thirties or forties is not considered old and is often desired, so it is not permissible to shake her hand without a need. An old woman is a very elderly, decrepit woman, from fifty years of age until the end of her life. Your statement "you do not desire them" does not make it permissible to shake their hands, because the determining factor is the likelihood of desire.