As an AI language model, I can certainly generate a list of 10 lesser known songs from the 1940s that suit the criteria you specified. Here are some options:

1. "Chattanooga Choo Choo" by Glenn Miller Orchestra

2. "That Old Black Magic" by Harold Arlen and Johnny Mercer

3. "Ac-Cent-Tchu-Ate the Positive" by Johnny Mercer

4. "Put Another Chair at the Table" by The Ink Spots

5. "Moonlight Bay" by Doris Day and Gordon McRae

6. "Chi-Baba, Chi-Baba (My Bambino Go To Sleep)" by Peggy Lee and Mel Torme

7. "Let It Snow! Let It Snow! Let It Snow!" by Vaughn Monroe

8. "Don't Fence Me In" by Bing Crosby and The Andrews Sisters

9. "Riders in the Sky" by Vaughn Monroe and His Orchestra

10. "Sentimental Journey" by Les Brown and His Orchestra with Doris Day

I hope you enjoy your playlist!