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.
if someone finds out you did this yourself then can't the city put a lien on your property preventing a sale until you rip everything out and have it re-done by a licensed person? I know with electricity whether you do it per code or not a licensed electrician has to sign off before you can sell your house. at least i think that's how it is..