So, this may depend on your definition of incredibly cheap, but picked up a (built in) battery powered cordless spray bottle on the river site for $24.
It's listed under the brand "airchr", though there are a bunch of other brands with identical sprayers. It's marketed as a plant mister. When i ordered it, I was afraid it was going to be a crummy auto sprayer like came on a bulk bottle of "Bug Barricade" (the Raid stuff to keep critters from wanting to crawl into your house) - that sprayer works, but sounded broken. This one is actually surprisingly nice - quiet and provides a really nice mist pattern. Planning on using it for pre-soak for rinseless washes. I'll update this when I get a chance to use in on a car - so far all I've had a chance to do was a quick detail of my toolbox at work. :laughing:
Probably also going to pick up another one to use for spraying ONR at home, I use it for cleaning all our hard floors. You can adjust the spray from a very fine mist to a straight stream. Just tried the straight stream, holding it straight out it sprayed nearly 20 feet (!).
Like I say, $24 isn't exactly the deal of the century, but you can spend $40 on a pump up hand sprayer that you have to pump up like crazy as you're working around a car.
Now if only I could figure out how to make it foam...