How does shaking someone's hand endanger the strategic interests of the United States?

It really doesn�t. It is smart, and it signals to the world that we are a rational country. It also looks better for us because (even though it is highly likely that a country with such a small military would do anything to antagonize us) if they did do something stupid, we would be more likely to have backing by the world because it looks like we are the good guys.