BTW it isn't in hijaz, but hijazkar - hijaz doesn't have a sharpened seventh. Because of the weirdness of Greek transliteration, it's sometimes spelt "hitziazkar" in transliterations of Greek sources, but isn't pronounced like that.

If Misirli Ibrahim Efendi wrote it, this may be of interest:

biography in Turkish

That site (surprisingly, given its coverage) only has one piece by him, and it isn't "Misirlou".

My guess would be that the tune is much older - it's an archetypal kind of melody for the hijazkar mode, which was known to the ancient Greeks and one of the commonest modes across India. Anybody noodling in that mode could come up with it. When I was learning the flute I used a tunebook by Quinto Maganini which had a piece which he said was a Greek lament from Sicily - almost the same tune but a slightly different rhythm, which he said matched a chorus in a play by Sophocles.