By kindly allowing a POD as early as 1943, I think you open the door to numerous "separate peace" scenarios where a surviving Nazi regime might be in a position to launch such a war later. To be considered WW3 rather than a mere extension of WW2, I think its safe to say a good period of time would have to lapse, though.
Now I could go into more detail, starting with the 6th Army escaping Stalingrad and bloodying the Soviets with an early Kursk, but I'm rather reticent to write much as I know this board is particularly hostile to all "Nazis do better in any way whatsoever" PODs, so I'll let others write up and get their scenarios butchered and called ASB

Still, my belief is that it would have been easy to get Stalin to agree to a separate peace, after all there were contacts to this effect as late as Kursk in OTL.
The western front would be more difficult, though if the 43 POD is early enough, you can technically remove the "unconditional surrender" doctrine too, which could have happened if the Germans seemed to have more momentum than they did in OTL. At that point, its not unthinkable that if Germany gets a favorable truce in the East, the Allies might consider the same in the West if the Nazis are willing to pull out from most of their western conquests.
No matter their gains, the Germans would then feel squeezed between two giant, militarized alliances who think they are evil. An arms race from day one is about a given. In order for the resumption of hostilities to be "WW3", I would say at least 5 to 10 years have to go by though. A good reason for the Germans to provoke such despite the amazing array of forces against them would likely be internal factors, such as economic or social collapse. Alternatively, strong evidence of mass-scale genocide in the Reich could prompt a resumption of hostilities which the West would still say was Germany's fault, if you consider this counts.
Most likely, the only way to prevent the use of nuclear weapons is to ensure all parties have them and make a clear deal not to use them first. Or maybe the war is initially solely German-Soviet and only the Americans have the bomb, presumably because the early Soviet separate peace made it harder for them to get close to, and spy on, the American program.