I recommend Transferwise [1](now just Wise) for getting money to someone in Ukraine. They've got low fees and the ability to send money to Privatbank cards. Used them many times, while in Ukraine and while in the US.
I look forward to hearing how this works out, to the extent that you're comfortable sharing details. I feel like probably escaping from a war zone might cost more than US$200 and currency exchange might be problematic at the moment.
1: https://wise.com/