Since it takes two to shake hands, no odd number of people can handshake, since one must be left out. Therefore 99 people cannot shake hands. Unless "handshake" means something unusual here, which...
Shaking hands.
According to Dummies.com, you should "shake just a couple of times." I don't believe there is any "correct" answer to the question. Personally, I think you should hold it long enough...