The way I see the arms proliferation going-the Saudis would get them from Pakistan. That is if Iran got them first and Israel didn't nuke them.
After that, I can see Egypt getting them-they have the resources and money, and withdrawing from the NPT would not be much trouble for Sisi, Turkey would be getting nukes at the same time.
Jordan and the other Gulf Monarchies would rely on the Saudi umbrella; Syria, Iraq, and Libya and Yemen are devastated war torn shitholes(well Iraq isn't as much these days but yeah its still a screwed up place), and so would not have any money or resources to devote to nukes(not that say Bashar wouldn't at least look into it). Lebanon is coming apart at the seams, and the Israelis would respond very harshly if they tried to get them.
Sudan-is too poor and now with the country's future an open question I don't see them trying for them.