Most are designed to be installed in windows, and as such have window type widths. Any that would fit between studs would be 5000BTU/hr or less since a very narrow cabinet limits the size of the evaporator coil.
Mini-split solutions only make a ~3" diameter hole in the wall and are generally quieter, and start at 9000BTU/hr for the smaller units. Lesser-name 13SEER units run ~$750, but you can get high SEER high HSPF cooling and heating 9000BTU heat pumps like a Fujitsu Halcyon or Mitsubishi H2i for less than 2x that. If you're up for a DIY installation it's not rocket science, but it's good to have qualified tech test & fully commission it.