Can I use the disk rotor from the current mechanical brake when I switch to hydraulic?
Yes this will be fine.
The only caveat I can think of is rotor thickness, if you look closely on a rotor or read the manual, you should be able to find the minimum thickness.
This is different for different manufacturers but shouldn't affect a hydraulic disc brake, they automatically adjust for pad and rotor wear and will happily clamp a pair of new pads together with no disc in between.
See this question about pad material. I wouldn't worry about that either.
The type of braking mechanism should make no difference in what kind of rotor to use.
As mentioned before, ensure the new brake pads line up well with the original rotors. If they are poorly aligned, you may experience brake-rub or squealing while stopping. Rubbing alcohol can be used to keep your pads and rotors clean and quiet.
In the end, rotors are fairly cheap and you can swap new ones on it you do not like the feel.