Is it possible to plug an AC into a kitchen stove hood exhaust?
It sounds like you are attempting to make your own version of a space air conditioner.  These are an air condition broken into two parts.  The first part is an outdoor box that is the size of a brief case and then the other part is the fan that blows the cool air.  The two pieces are connected by about 10 feet of semi-flexible tubing.  They plug into a standard outlet and are meant to only cool small areas such as a room or office.  We used them all the time in Afghanistan.  We could retrofit anything to hold one - tents, conex boxes, sheds...  You would not need to cut holes in the walls for the tubes.  Should be able to run them through the stove hood as long as you don't turn the fan on.  I think it was called a chuga or something.  Works create and they were not too expensive.