The most prestigious shliach can indeed not be gezhe. You can be gezhe and not even be an observant Jew. So long as your grandparents urinated in select Russian/Ukranian towns. Depending on which town any gezhe Lubavitcher stems from, the other towns won't count.
Not sure about the Ukranian towns (Yekatrinoslav/Dnepro doesn't cut it, and I'm doubt if Nikloaev does). Maybe Belarussian. It's basically a handful (Klimovitch, Nevel, Beshinkovitch, and maybe another 2 or 3 that I can't think of at the moment. The fact that you had famous Chassidim in Nikolaev, Homel/Gomel, Horodok/Gorodok, etc. doesn't make those Gezhe. The purebred is a product of a select few towns).