Well, while everyone is weighing in here...
Remember if you cut your stone you must header off one way or another over the hole. The stone you leave over the unit must be supported as are your windows, doors, etc. You can get the stone out with careful demo and actually leave the stone above the hole for the unit.
But without a header (usually some angle iron), one day you will come home and it will all be in the yard. You cannot canitlever rock unsupported. Remember too, that you must header off your inside wall as well. Then of course there is a problem to consider if you have to remove some of the wall support straps that attach the stone wall to the wooden frame wall.
To prevent misunderstanding, I know you can use stone for vaulted ceilings, etc. without any lintel or any other kind of visisble support underneath. But keep in mind in those instances it was originally laid that way by keying in the stones to support one another. He is talking about chopping a hole in the existing wall.
On another tact, one of my buddies bought a free standing unit (on wheels!) at Sam's club and it works quite nicely. It is 10,000 btus, and uses the air from the room, and only needs a six or eight inch exhaust which he poked a hole in his wall to accomodate. You could easily put this unit in your shop and exhaust up to the attic.
Robert