Do hydraulic road brake levers exist that do not include shifters or dropper post buttons? I have a single speed bike (Genesis Day One ~2013) with mechanical disc brakes.

I would like to upgrade to hydraulic disc brakes.

Do hydraulic road brake levers exist that do not include shifters or dropper post buttons?

Shimano &amp; SRAM levers appear to all be designed to work with their geared groupsets. Magura don't appear to do road bike brakes.
Currently, TRP Hylex are one of the only drop bar brake lever (without gears) that has a hyraulic master cylinder. Magura HS66 is another, but these are pretty rare. 

Other options include:

Cable actuated hydraulic calipers. These are connected by cables just like normal caliper but the hydralic master cyclinder is at the caliper end, so any drop lever will work. TRP Hy/Rd are the most popular version of these, but other cheaper brads also exist. 

Yokozuna Motoko Cable-Pull Hydraulic Disc Brake



Cable actuated master cylinders. These as master cycliders which are attached to the stem or handlebars and are also actuated by cables, so any drop lever will work. Examples of this are Giant's Conduct and Hope Tech V Twin System

Giant Conduct



Hope V-Twin