Most do it while pushing but the nurses just clean you up without saying anything. They've seen it all so don't be embarrassed. :)
Its very common believe it or not, the nurses will clean you and continue, that is exactly what youll be doing when pushing, push like you have to go poop, i doubt your partner will freak out, and if he does just throw the "you fu.cking did this to me a.hole card" lol i did it, everybody goes to the bathroom