I am looking for both the complete lyrics and more information about a song my mom sang to my sister and me in the early 1950s. We called it Cuddly Pets and what we can remember is

Cuddly pets are cute and tidy
Cuddly pets don't need a diddie
Junior's ooky, junior's wet
Trade him for a cuddly pet.

We know there were several verses. My mother found this masterpiece in a science fiction story that she read in one of the science fiction magazines of about 1950, in a tale about android pets that involves the patenting process. The song was part of an advertising campaign. The story may have been titled "Love and Gratitude," or maybe not. We would love to find the story, because one of the characters in it was modeled after my Uncle Herbie, who was a federal judge at the US Patent Office Court of Appeals. Apparently the author knew my uncle, and was familiar with the patent office. Unfortunately, Herb is no longer with us, and no one else in the family has any more information.My mom, my sister and I would love to know more, and to read the story, if possible.