Almost all of the documentation that I've read seems to suggest that a controller is required, but I've been assigned to sell my employer's old 1000's and finally get rid of the ancient 4400 series controller. Can I reset/unjoin the Aironet APs from the controller and have them run in standalone mode? Does a standalone mode even exist?
Nope. That entire product line is "lightweight" only, so no autonomous/standalone operation mode is possible on that hardware.
The product line's end end of sale as well, so I don't know how much your employer expects to get for them, but they're going to be disappointed. Seriously, a quick search on eBay shows them being offered for as little as $19.95 and as much as $50, so it's probably not even worth the time to try and sell them.