Hydraulic disc brakes and road shifters
You need a hydraulic shifter to use a normal hydraulic disc caliper as there is a piston that moves fluid which a mechanical shifter will not have. 

There are mechanical to hydraulic systems where the cable from a regular shifter actuates a hydraulic system on the caliper itself. They are usually a little more bulky looking. This would probably be your best option if you can't get hydraulic brifters but must have hydraulic calipers. 

You can however use your mechanical shifters with cable pull disc calipers as you noted. This works well. You don't have the hydraulic advantage of nearly zero friction in the system. You don't get that with cable to hydraulic either but you may or may not get better modulation with a cable to hydraulic.