Dorothy Shaver, who became President of Lord and Taylor in 1945 and was one of the nations' best-known women executives in the 1950s, was born in 1893 in Arkansas. She was educated first at the University of Arkansas, and later at the University of Chicago. She and her younger sister Elsie began marketing Elsie's handcrafted dolls, the "Little Shavers", in 1922. Due in no small part to the successful marketing effort headed up by Dorothy, the dolls were a commercial success, and drew the attention of executives at Lord and Taylor, a large department store chain based in New York City. Acting as her sister's agent, Dorothy sold some of Elsie's fashion drawings to Lord & Taylor, and thus began what would become a fruitful collaboration. By 1931, Dorothy had been named a Vice President of Lord and Taylor. AT the helm of Lord & Taylor, she helped to inaugurate "The American Look and helped to establish the "Costume Institute" at the Metropolitan Museum of Art in NYC. She was named President of Lord and Taylor in 1945, the first woman ever to hold that position. Dorothy Shaver died in New York in 1959.It looks like someone is trading on the Little Shavers name here.
I suppose it's possible that the expression predates all this, but I thought it was interesting anyway.