"Are You Lonesome Tonight" is a song that's associated with Elvis Presley, but it was written in 1926 (not sure about WWII-era recordings). "Tennessee Waltz" just misses; it was written in 1946. Another one that's close (even closer) is "Carousel Waltz." The Rodgers and Hammerstein musical "Carousel" opened in 1945. (This one is a Viennese Waltz, not a slow Waltz.) "Santa Lucia" is another possibility. It's a traditional song written in the 19th century, and recorded by a lot of people (Perry Como, Mario Lanza, and of course Elvis).