I don't know how "Compact" the air conditioner is that you are talking about, but you can visit the dealership, get a model number off the unit, and then search for it on a place like Amazon.com.
AS for through the wall units that do not have air intakes on the side of the portable air conditioner, they are called through the wall, and have a wall mounting sleeve that is sold separate from the A/C unit that slides into that sleeve.
Here is a commercial 115 volt through the wall A/C.
AcWholesalers.com You can select other through the wall. I did not find a sleeve - unless I clicked on the LG A/C and it has a wall sleeve for $106. Intake is on one side of the outside grill, the exhaust is on the other.
It is quite large, I think it was 24" wide and 14" tall. Is that the size you are looking for?
Most portable A/C window units, such as found at Costco will have air intakes on the side, and therefore can not be flush mounted with the outside wall. Through the wall A/C can be flush mounted with the sidewall, and the units slide in and out easy for service, or to exchange units.
Good luck,
Fred.
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