Broadway becomes him, too: “Martin Short: Fame Becomes Me” is set to open at a yet-to-be-determined Shubert theater Aug. 10.Conceived by Short and the “Hairspray” composer-lyricist team Marc Shaiman and Scott Wittman, the musical mock-autobiography isn’t a solo show. An ensemble of four performers backs Short, as does onstage music director Shaiman, who also composed the tunes. Wittman, who co-wrote the lyrics with Shaiman, helms the production. Short and Daniel Goldfarb (“Modern Orthodox”) wrote the book, and Christopher Gatelli (“Altar Boyz”) choreographs. Production tries out at the Curran Theater in San Francisco April 25-May 21, and then at the LaSalle Bank Theater in Chicago July 5-16.