And you expect us to sit here and design the whole thing for you (even worse if it's a school assignment)? You're going to have to tell us what exactly it is you need help on.
By the way, 10mV ripple at 2kV output is 0.0005% ripple which is almost impossible (if not outright impossible) to get with current technology. It would be better if you specified your ripple as a percentage since it is over a range of voltages rather than at a fixed voltage.
You also say no constant current as a specification. Do you mean no current limiting? Or do you mean you do not need constant current? Becuase if this is what you mean then you need to review your understanding of power supplies. YOu describe what is a voltage supply, but then say you do not need constant current (which by definition cannot be part of a voltage supply). You always adjust the voltage to regulate the current, or adjust the current to regulate the voltage- you can't have both regulated voltage and current at the same time.
Linear type is not huge heavy and expensive because of the transformer. It's huge and heavy because the linear stage needs a giant heatsink. You only need 10mA of current so the transformer is going to be TINY. Just follow it with a switching stage instead of a linear stage. The transformer provides isolation from the AC line which also makes it a lot safer.