To go back and answer your initial question however, "can kokyu-nage be done without kokyu?" I would have to ask, how do you define kokyu?
That's fine, Chris, that you "have to ask" that question, but that's not the original question. In the post of mine that you're actually quoting from, I define the "breath" and "timing" issues that are a part of kokyu, but not the core power. The core power is going to be the trained skill of jin, or more generally "ki", as is shown very repeatedly in Tohei's "ki tests". That should be enough of a definition for you to go on and make your point. If you don't think the core power being shown by Tohei is a necessity for a throw to be a kokyu throw, you have the option of saying it publicly.