Stauffenberg- "He Joe, we have Adolf here for you if you end the war."
Stalin- "Give him to me, I love what he's done with the mustache"
In my opinion, it would work. Maybe they can arrest him then shoot him. I think it might be better for the Germans strategically, one of the main flaws of the Nazis were that Hitler believed he was a military genius, when he was not.
He believed in fighting to the last man, no retreats. A strategy that ultimately failed him.
With the Military in command essentially, they can keep the Allies at bay in hedge country in Normandy. They might also be able to slow down the Soviets.
Rommel would likely be put in charge of the Armies, since he despised Hitler. The Death Camps would be put to an end as soon as the SS was disposed of. Civil War though deep within Germany would ensue between the Army and the SS.
Maybe by the end of the month, they would call for a ceasefire to discuss surrender.
Likely post war Germany...
Germany keeps Alsace-Lorraine, Luxembourg, Austria, Czechoslovakia, and Denmark. Italy is to be returned Libya. Somalia and Ethiopia will remain in Allied hands. The Vichy Government will still retain control. In southern france.
As for the Eastern Front, I am not sure weather or not Stalin would be willing to surrender, but if peace with the Western Allies is made, by the time Operation Bagration came along, it would be stopped in its tracks with the military in command.
I could see possibly after a massive stalemate on the Eastern Front, the Germans would use their old WWI strategy to win in Russia. Take some land, hold it for a while, then move on.
This might cause the Russians to sue for a Ceasefire along the Ribbentrop-Molotov Agreement in 1939, or a Brest-Litovsk Style treaty.
In the Post-War, I see a lot of happier Germans, Germany won't be split and a Cold War between Germany/Western Allies Vs. The Soviet Union occur.
With the war in Europe over though almost a year earlier, they can send troops to the Japanese and the War in Japan would likely end on the same way it did IOTL.