Asalamu Alykum
Dear Deliverance
Just want to point out a little information about the Quranic guidance. I do believe the Quran allowed for humans to use their minds and do form proper actions around Quranic commands using their own intellects.
The Quran seems to not want to program a ritual or implement gow to organize concepts that are commanded. That would almost be akin to us being robots and never using our own faculties.
It does seem sometimes that the Quran has allowed us to use our reasoning to establish proper practices surrounding certain commandments.
That being said, the Quran is not giving details on the details of how to salute people. Arguably every situations and certain people would possibly greet each other differently. Greeting ones mother, father, wife, brother, sister, sons or daughters might be very emotional and could be with hugs and kisses where greeting strangers or ex-wives ir husbands or married women might be with salutations of peace or a simple hand shake.
If ones customs is to handshake then there seems to be no problem with it.
If peoples customs is to just say Salam or Peace or Hello with a hand gesture or wave and not shake hands with the opposite sex then also that is to be respected.
As long as the greetings stay within the Quranic values and decency.
Hope that helps Insha'Allah
Salam