From first hand experience of Ukraine being one of the most corrupt nations on earth can just anybody get traffic rights in/out of there without paying appropriate, and significant, "back handers"?
Would have suggested Aerosvit on their KBP/JFK/KBP schedules but they went out of business a while back.
Your post suggests you're just moving people in one direction thus you're going to be paying for significant empty legs, probably cheaper to move the 400 on various scheduled services such as KLM, Austrian, Lufthansa, Swiss, BA, Turkish, Alitalia or whatever ... unless there just happens to be an idle B747 sitting around Kennedy Airport doing nowt else.