I'm pretty sure that anyone who served in Korea and Vietnam, as well as their families, would consider them to be
major conflicts. Personally, I think that 2.8 million deaths in Korea and 5.2 million deaths in Vietnam speak for themselves.
Regarding fewer deaths from war since 1945, you should consider reading this. It may change your mind:
http://users.erols.com/mwhite28/warstat1.htm
As ETR already said, the Cold War was, at it's core, a series of wars and conflicts over who was going to put their nukes where. We had ours in western Europe. The Soviets would spend the next 40 years trying to achieve a reciprocal standing, resulting in the majority of the conflicts listed on the above website. Of course, we not even need to mention the Arab-Israeli conflicts, the invasion of Iraq, and issues with Pakistan, India, China, North Korea and Iran, all of which are directly rooted in the possession or manufacture of nuclear weapons.
In short, the use of the Fat Man and Little Boy bombs did indeed prevent a horrendous and bloody invasion of the Japanese homeland that would likely have made D-Day look miniscule by comparison, but claiming that nuclear weapons have reduced the need for nations to engage in warfare is fallacy.