I would prefer a kid to shake hands after a match but if they don't I don't have a problem with it. I have never seen a coach not shake or give a fist bump to a kid that went to shake their hand. If this does happen they are wrong and are taking it way to personal.
Also if you are that worried about a "communicable diseases" then I think you are in the wrong business.
As far as comparing wrestling to any other team sport it's difficult. Shaking hands after every inning would be more like shaking hands after every period or every time the whistle was blown.