i'm a firm believer in pushups--though i do them for sports performance reasons, not for cosmetics. maybe you could get by with only dips. matter of fact, i had a boxing coach who had his boxers do only pullups and dips--he thought they were more effective exercises than pushups--so you're not the only one who thinks that way.
or, if you do hindu-pushups, they are like half dip, half pushup, so you get the best of both worlds.
you can definitely build mass with bodyweight exercises, not a huge amount, but it's possible. herschel walker would do hundreds and hundreds of bodyweight exercises everyday--he had an incredible phsyique.
the great gama had huge pecs--the result of hundreds of hindu-pushups everyday. he also wrestled all-day.
kimura, japan's greatest judo player, had an incredible upper body. he did 300-500 judo pushups everyday (kinda like hindu-pushups). he also did judo 13 hours a day.
i know someone who does over 1000 pushups in a day, 3 times a week. and they have plenty of mass.
so, it's possible, but you have to do 1000s. get's kinda boring without making it into a game.