Yes you can run a wood stove pipe through a wall and they make a through the wall kit for about $300.00
I have my wood stove pipe going through my wall right now but I didn't use a kit but I did have a double wall stove pipe that was given to me and I cut a hole and ran that through the wall for the insulated part and then put a single wall elbow on the end of it pointing downwards to prevent wind from getting into the pipe.
That's the cheap safe way of doing it. You must have that insulated pipe to go through the wall or you'll start a fire. Never run single wall stove pipe directly through a wall. Unless it's an all metal building.
It's best to use the stove kit if you have the money but sometimes you have to do it the best and safest way you can.
I plan to buy the wood stove pipe kit when I get the money to do so.