What is the Shar'i view on the involuntary discharge of drops resembling semen, without desire, after shaking hands and conversing with male friends and acquaintances? Is this forbidden, and how can one get rid of it?

If a fluid is discharged involuntarily, and you do not experience lust when shaking hands with your brothers or speaking with them, then there is no sin upon you, no accountability, and no need to refrain from that. You must wash off whatever of it has touched your body and perform ablution for prayer, but ghusl (definition) is not obligatory.