I have a wood stove that I'm going to use in my work room that is on the first floor of my house. I was planning on running it out the side of my house and then the chimney go up next to my house. I have a wall thimble to go through the wall, but my question is, can I use single walled pipe for the chimney? It wouldn't be touching the house.
As a wood stove owner I can tell you this is a bad idea. You need to look carefully at the wood stove manufacturer's requirements, but most wood stoves need a large draft to operate correctly and loss of heat through a single wall pipe causes too much loss of draft as well as creosote problems eventually leading to a chimney fire, if you can manage to keep your stove lit.
Whatever type of pipe you use, make sure you maintain proper clearance. It's more than just a question of "touching", and single-walled pipe may have clearance requirements of 18 inches. Double-walled pipes are less, maybe 6 or 8 inches.
Having said that, single-walled pipe is probably not a good choice for the outside chimney. The concern is not so much heat causing the house to catch on fire (because you must maintain the aforementioned clearances), but that cold outside air will cause the exhaust gasses to cool, which will make it hard for the stove to vent properly. You want the hot exhaust gases to pass up through the chimney quickly, but if they are cooled once they exit the building you can get the colder gases trying to sink back into the stove. Poor draft leads to smokey, hard-to-start fires, creosote buildup, and possibly flue gases backing up into the room. Just did some quick research and it turns out that both single- and double-walled stovepipe are only permitted indoors. When you transition to the outside through an insulated thimble you must use "Class A Chimney", which is an insulated product.
Finally, if your stove or local building codes require double-walled or something else specific, that's your answer right there. A neglegantly-installed wood stove is a huge fire hazard, and I doubt your homeowner's insurance would cover a fire caused by an illegal stove installation.