Anything on YK (deoraiso) is ossur. Less than a reviis of water, especially to take pills, on the 4 minor fasts (all derabonnon), is allowed by just about anyone. I am not sure about 9 Av which of course is also derabonnon.
OB Creedmoor: The Admou”r meCreedmoor says that Yom haAtzamois has the same status as Yom Kippur and that anyone who even has a drop of water on Yom haAtzamois is chayav kooreys.