The Collaborative International Dictionary of English v.0.48:

Sheik \Sheik\, n. [Ar. sheikh, shaykh, a venerable old man, a
   chief, fr. sh[=a]kha to grow or be old.]
   The head of an Arab family, or of a clan or a tribe; also,
   the chief magistrate of an Arab village. The name is also
   applied to Mohammedan ecclesiastics of a high grade. [Written
   also scheik, shaik, sheikh.]
   [1913 Webster] Sheil

WordNet (r) 3.0 (2006):

sheik
    n 1: the leader of an Arab village or family [syn: sheik,
         tribal sheik, sheikh, tribal sheikh, Arab chief]
    2: a man who is much concerned with his dress and appearance
       [syn: dandy, dude, fop, gallant, sheik, beau,
       swell, fashion plate, clotheshorse]

Moby Thesaurus II by Grady Ward, 1.0:

28 Moby Thesaurus words for "sheik":
   Casanova, Don Juan, Lothario, Romeo, amoroso, beau, boyfriend,
   caballero, cavalier, cavaliere servente, esquire, fellow, flame,
   gallant, gigolo, inamorato, lady-killer, love-maker, man, necker,
   old man, petter, philanderer, seducer, squire, sugar daddy, swain,
   young man