It’s something I had heard before but didn’t see an attribution (though the perjorative “boy” referring to Black men vs “hand” for white men seemed to me to give credence to the idea). The Rancho Los Cerritos Historic Site makes the same claim:

Originally, White cowboys were called cowhands, and African Americans were pejoratively referred to as “cowboys.” African American men being called “boy” regardless of their age stems from slavery and the plantation era in the South. Many southerners moved to the West and westerners would have been familiar with southern racial etiquette. So, it is no surprise that the racial issues prevalent in the North and South were also impacting the American West.

While they do provides sources for that blog post, they don’t directly attribute that statement to a particular work. However, this clip from PBS is an interview with Tyree A. Boyd-Pates, curator at the Autry Museum of the American West and he also states that “cowboy” would have referred to a Black cowhand.