I'm a lazy brewer, I rinse out the carboy with about 1/2 gallon of water, then add another 1/2 gallon and some oxy clean or PBW and scrub it out with a brush, if there is dried on stuff I fill the carboy with water and PBW and let it sit overnight and then everything dissolves.
I don't see why you need a sprayer set up unless you are cleaning more than a couple of carboys at a time.