Wallis and David (to give him the name he was personally used) wed in 1937. This TL posits she died in 1936; means they never wed. In fact, she wasn't FREE to marry him until spring, 1937. You keep saying "new" wife, he would never had had one if this occurred.
No, I don't think he would have married. He didn't want to marry anyone suitable; that was the appeal of the Freda Dudley Wards, the Thelma Furnesses, the Wallis Simpsons, they weren't suitable.....Wallis, once dead, would be the impossibly 'high' standard to which all other women would be measured.