Some Ukrainian banks have dollar ATM?

No dollar ATM, but if there are, they are empty since the crisis began :)

If You have dollars at current currency account in acts with that amount you are very limited to allow storing/selling on the stock exchange/escrow line. Bring them You can only by double exchange, i.e. sale of foreign currency by the Bank on the stock exchange -> transfer on current account in national currency -> transfer to card account -> withdrawal at ATM -> the purchase of foreign currency (card and ATM if you want you can skip).

ATMs of FUIB. They are usually hanging sticker with information about the possibility of withdrawing USD.

OTP bank