I searched The Lester S. Levy Collection of Sheet Music for words like "Arab" "sheik" and other associated words, and found these songs:

Araby.
Araby's Daughter. From "Lalla Rookh."
Bagdad.
Burning Sands. The Answer to "The Sheik."
Fly to the Desert, from Lalla Rookh.
Geo. Schleiffarth's Vocal Compositions. No. 7. We Draw the Line at That.
Lovin' Sam (The Sheik of Alabam)
Marie Cahill's Arab Love Song.
Tahmineh. Amour d'Orientelle.
The Rose of Algeria. Twilight in Barakeesh. (Zoradie and Chorus).
The Travelers. My Arab Lady.
While the Incense is Burning (I Dream of You).