A 27-speed bike has a 9-speed rear.
Any Shimano 9-speed shifter should work.
You will need a new bar, new stem, shifters, brake levers, new cables and housings (may come with the shifters and brake levers), and grips.
You may need to rig up some Travel Agent pulleys to reduce the cable pull, or get some brake levers that are compatible with caliper brakes. Otherwise your brakes may be a bit touchy. Road levers pull half the cable as MTB levers.
What you are considering is quite a bit of work and not much real gain. Most people go the other way, switching flat bars for drops to get more hand positions.