I second the notion of Habitat, or a secondhand building supply shop, for a door. Worst case, get one that's too big and cut it down to size. You will be surprised at how cheap a door can be.
My other thought - put a "cat flap" in the shop door. This won't be as ugly or home-made looking as a hole you cut, and it's not an outrageous thing to have on a door, either. The kit to install it will cost $20 and will come with trim to hide and seal the ugly cut edge. Then when you need the AC, just stuff the hose out the cat door. When you don't need the AC, it's not a big deal.