Hi Neil,
The dates you gave are outside of the windy season in Oahu. It finishes in September. Staying in Waikiki you may be lucky to get some Kona winds which are favourable on that side of the island, but to the best of my knowledge, no one hires kites on Oahu and definately no kite shops on Waikiki side.
You will have to visit Kailua for all the kite shops with the exception of Kite High (Andy Heaton) in Haliewa (North Shore).
It's swell season at that time of year, forget kiting go rent a surfboard!
Good luck,