You have me very confused.
You bought a "through the wall". I would interpret this as a
motel type unit about 3 feet wide by 2 feet tall. It is smaller
than what is there now. Motel type units come with their own
"sleeve", pull out the old one, use the new one, close the hole
around the new sleeve with foam, insulation, trim, whatever.
You ask about a window unit. These units are designed with an
indoor and separate outdoor portion. As long as the outdoor
portion is outdoors, you can install in any appropriately sized
hole. It again comes with it's own "sleeve" , close the hole down
to the sleeve.
Keep the whole world singing . . . .
Click to see the full signature.