Simeon Saxe-Coburg-Gotha, who reigned as king of Bulgaria from 1943 to 1946. He was only nine when he was forced to abdicate, so his reign was mostly ceremonial.
Tenzin Gyatso, the fourteenth Dalai Lama, who has reigned since 1940. He became Dalai Lama, so I would think during World War 2, his reign was also mostly ceremonial.
Queen Elizabeth II (born 1926) did not ascend to the throne until 1952, after the death of her father. She was, however, enrolled in the Auxiliary Territorial Service during the majority of 1945.