Upvote:0
Here, 'International to international' section says nothing about passport check. If you google for something like 'kbp transit visa', most results (often notably old) suggest you don't need a visa if you don't change terminals (if the terminal you arrive at and depart from is the same, and if it is terminal D).
You might probably want to contact the airport (the first link I gave displays phone numbers on the top of the page) and/or the nearest Ukraine consulate for a better clarification.