Personally, I have no problem with doing away with handshakes all together. Half the men I shake hands with want to make the gesture into some sort of strong man contest. I have a glitchy bone in my right hand, courtesy of an old break, and it doesn't like to be squeezed.

I'd rather see bowing adopted as a world-wide greeting. Bowing connotes humility, whereas handshakes often connote a desire to dominate. Western society could use a bit more humility and less trying to be dominant.