It took a while but I eventually did find a song in Turkish arranged for the ukulele.
Unfortunately, the Turkish ukulele player, Özen Özdemir (ozenozdemir), remains invisible throughout the song.
The song is called Kim Görmüş (Who saw ?). After some research, it seems like the text is a Turkish translation of a poem or Rubáiyát by Omar Khayyám, a Persian poet, philosopher, mathematician and astronomer who lived between the years 1048 and 1131.
For those of you who would like to investigate Turkish and Turkey a bit further, here is a video of Turkish street performers singing for nature (no ukulele).