Honestly, I would recommend just doing it yourself. Especially if you have a contractor pull in the electrical connection for it. I installed a pre-charged unit in a much more complicated attic setup (condenser mounted to outside wall on second floor, 20' of refrigerant lines run with lots of angles) and the whole thing took 6-8 hours with no experience. Mounting it to a shed where you're basically just cutting a hole in a wall and the indoor unit and outdoor unit are in more or less the same location should be extremely straight forward. The unit cost me less than $1k five years ago and has been running perfectly ever since.

Pulling in the electrical connection is actually simpler. So you might as well do that yourself too.