Good question. I don't see the Germans being completely free of a North Africa/Middle East commitment even if they captured Alexandria or the Suez Canal. British Empire forces in the Middle East were supplied by convoys around Africa and from South Africa, India, Australia, New Zealand, etc. Even if they were pushed back to Sudan, Palestine, Syria, Iraq they would still be there, planning to retake their lost territory and forcing the Germans to maintain sufficient forces to hold them off. Japan's entry into the larger war stemmed from their ongoing war in China and the economic sanctions imposed by the United States. The absence of a Russo-German conflict would not seem to change this. Most of the British Empire's military power would still be tied up fighting the Germans and Italians. The Japanese would have installed themselves in Vichy French Indochina. No doubt having Russia tied up in a life-or-death struggle with Germany was helpful, but all of the Russo-Japanese conflicts had been initiated by the Japanese; they could feel reasonably safe about their northern flank while striking south to obtain the resources they needed. Historically the opening of war in the Far East dragged British Empire resources away from the Middle East, to the benefit of the Germans, and that would still be true in our current scenario. So we come to the question of whether Hitler would declare war on the United States, his greatest error in the opinion of many including myself. Historically he was fighting a major war with Russia, which had just taken a disasterous turn with the Soviet offensive beginning December 6. In our scenario, he would be preparing to launch the attack on Russia in spring 1942, with the confidence that it would collapse once he kicked in the door. In his mind, the danger of fighting both America and Russia might appear less than it did in real life.