Re: European Theatre
WWII ended in the European Theater of Operations (ETO) in May, 1945. So if he was killed in December his death would be non-battle. If he died from wounds suffered during the war that would be battle related.
The difference is important. The position of all units in combat is known and can be determined from the unit's combat chronical. Once the war is over the occupation forces can be deployed widely almost anywhere in Western Europe. To sort things out in the second situation you would need a record of the soldiers death generated by the military.