"Exotic" is indeed in the eye of the beholder. To me, a sax is a sax is a sax... ;) (ducking & running for cover lol)
Shehnai, Duduk, Ciaramella, Khene, Low D whistle, Sei Palmi Zampogna, Launeddas, Egerlander Bock, Veuze, Gudastivri, Ney-Anban... these are the exotic woodwinds...
Actually...