“Not only that, it may not even be a Yiddishe minhag”
Ouch. Shaking hands is quite Jewish and is as old as the earliest Rishonim and possibly the Gemara. See the Rosh’s quotation of Rabeinu Hananel on BM 74a. We mention it in hatarat nedarim. It is a symbol of agreement and often has far-reaching contractual obligations associated with it. As a Jewish social gesture, it affirms religious solidarity. It would be quite unfortunate if it becomes extinct.
וגם הנעשה בתקיעת כף