For argument’s sake let’s say you lost your nose in a tragic cheese grater accident. The entire fleshy part that protrudes from your face is now gone. Can you still smell? Are the smell receptors in the skull or were they in the “nose” part that’s now pencil shavings on the floor?
Dogs and cats lack the protuberant nose of humans, and they have a far better sense of smell than we do, so that should answer that question. The great apes also lack the protuberant nose of humans.
The function of the fleshy part of the nose isn’t really related to smell at all. It’s to warm and humidify air before it reaches the respiratory system. Humans probably developed it when they moved into the dry savannas of East Africa from their former moist forest environment.