Yes: mice really do sing. Scientists have recently argued that males in particular sing to attract females. But singing mice were popular stars long before science took them seriously. In 1843 one was summoned to Buckingham Palace to sing for Queen Victoria's children. Around 1871 a New England minister actually got two mouse songs scored on paper. And come 1937 radio listeners could hear an English and a Welsh mouse singing a duet, competing against America and Canada in the first ever Transatlantic Singing Mouse Competition. And yes, there is a recording. If you can get the American Library of Congress to release it, we could have another listen. Meanwhile, you can hear an unforgettable human version of the 1871 Wheel Song from my friend Tori Longdon, professional singer and conductor, over on youtube. 

https://www.youtube.com/watch?v=JVccO6LiXN8