Wa alaikum assalam
Shaking a woman's hand is a cultural habit for some communities to underpin a formal greeting or departure. It is not practiced with any sexual intent. If a woman's hand is held with intimate intent, then that is a totally different matter.
There is no Quranic prescription that I know from where it can be inferred that a woman's hand is an object of coverage or that it is inferred by reasonable deduction that it is forbidden or discouraged to touch.
Even the verb 'lamasa' (touch) in the context of verse 5:6 and 4:43 in the expression 'lamastumu'nisaa' has a context and is a reference to sexual contact.
I hope that helps, God willing.
Joseph