Will a small, narrow nose cause breathing problems? (photos)

Hi, I have decided to do rhinoplasty and made an appointment with plastic surgeon. He said he would make my nose narrower, remove small bump, lift it up and make it concave (a bit like sky slope). He is known in my country for making small noses with sky slopes. Many people on forums say that they don't know if those people can breathe on such small noses, can that be true? Narrow nose with sky slope, can that cause problems with breathing and, later, lead to saddle nose formation? Thank you :)