I think Korea could be solved by China and USA giving each Korea a number of divisions(after being asked of course). The USSR should also have to approve the war(as Stalin did) or the Soviets will not bless it. If they do they should send equipment(give them supplies and perhaps a fighter squadron or two).
This would give South Korea and North Korea control of the volunteers and the great powers are kept out of war. If South Korea is going down and the US declares war on North Korea(only if), the USSR should be given a choice to start a world war(declare war on America) or increase North Korean support) this could be the other way for North Korea as well.
The Suez should be fought purely through events, the USSR and US asked to denounce the invasion. If they do France and UK will be asked to back down(the ai will generally do so) or go into a real war with Egypt(and be expelled from NATO?) If they do the Soviets should be given the choice to send aid(perhaps a division of volunteers, supplies, etc.). After certain conditions are met the Suez could be surrendered through an event by Egypt.
Vietnam is harder. I think that mainly events should govern the war, perhaps the war could be fight between the two Vietnams with the South being given troops by the US(like suggested for Korea). Depending on which provinces are govern by which certain events will fire making the war winnable for each side, depending mainly on actions taken by China, USSR, and US. If the US are winning the Chinese might send hordes of troops(like in Korea) to beat them back and then America might be asked to bombard southern China, if they do the Chinese might declare war and the Soviets might give the Americans an ultimatum to leave Asia or have a full scale war on their hands.
This kind of solutions will be best for the odd wars the cold war mod timeline contains.