This particular phrase is SO common that I suspect it's used primarily because the artist needed a quick rhyming phrase and didn't have time to think up anything original.
Sugar Hill Gang
used a slight variation in "Rapper's Delight
just throw your hands up in the air
and party hardy like you just dont care
In addition to using this phrase in 1979 (first usage?), they have the honor of being the only group I've ever heard use "throw your hand in the air" and rhyme it with ANYTHING other than "wave them like you just don't care". Both by using "party hardy" instead of "wave" and also this rhyme...
then ya throw your hands high in the air
ya rockin to the rhythm, shake your derriere
ya rockin to the beat without a care
with the sureshot m.c.s for the affair
That's three different rhymes for "air" other than "wave them like you just don't care"...