The image of the Jew with the hooked nose was a propaganda tool created by the Nazis.
The following image is from a 1938 children’s publication in Germany called Der Giftpilz:
Demonization or dehumanization of the qualities of a group is pretty common in propaganda. This is why much of the Nazi art and media portrayed the Jews with rat noses or ears that resemble devil horns.
You’ll find that large noses are typical among people of all backgrounds. The type of nose you’re describing is common among just one of the many groups of Jews. Like any community separated by culture and geography, their gene pool is fairly narrow and certain recognizable characteristics are concentrated.
Of course, there are many Jews from the same group and all other groups all over the world who lack the stereotypical large nose. Also, you mentioned evolution, but that’s not really how evolution works. Evolution functions on a much larger scale than the amount of time Jews have been on Earth. If your notion of the nose size having connection to "salty air" (it’s the sea that contains salt, by the way, not the air), all people living near the Mediterranean would share the same feature.