WW3 starts relatively soon after WW2. Berlin crisis, Suez Canal, etc. Before we have enough of a nuclear arsenal to send civilization back to the Stone Age. We still do a lot of damage, but it isn't the end of civilization. The Communist Bloc loses, and Eastern Europe becomes democratic. Communists stay in power in Moscow because Russia is too hard to occupy and subdue.
Between the damage caused by the war and the sheer horror of WMD, all countries become less warlike for at least the next couple of decades. Colonialism ends slightly earlier as Europe can't afford it.
The Saudis start funding radical Islam sooner, leading to the brand of terrorism we know in OTL. But post WW3 you don't have the Mossadegh coup, so Shi'ites (who are historically tolerant) don't become associated with ayatollahs.
When WW4 breaks out, it's Libya, Egypt, Saudi Arabia, Iraq, Somalia, Pakistan, Afghanistan vs Iran, Israel, western Europe, Ethiopia, and the US. Maybe the USSR jumps in due to trouble on its southern border (on the side of its WW3 enemies, especially if a Khrushchev type is in power).