Phil, what do you mean by "two push buttons"? They all have two...
John Young trained two years with an Omega Speedmaster 105.012 which was missing the lower button. Moreover, many astronauts didn't care about the Tachymètre bezel, which was useless in space...
December 1966, during Project Gemini NASA astronaut feedback, the astronauts wanted a more practical Speedmaster, better legible dial and a "60 seconds" bezel... In May 1970 this feedback was repeated after the Apollo 13 mission and it took one more year until NASA finally came with a practical "60 seconds" Speedmaster for the prime & backup Apollo 15 crews...
More on that story soon...