So, you're basically looking at building an offset smoker. Steel is the standard material for the smoke box. You could do wood, but I would do a double wall, overlapping board to make it as air tight as possible. Wood limits you to 400F MAX temp. Not a problem if smoking is your goal.
Steel doesn't care. For steel, old propane tanks work well, or you can fab a box out of 3/16-1/4 steel. The door needs to seal in some fashion. Like a rope gasket, or silicon gasket. And you need a damper on the stack and air inlet to the firebox. Temp control is PARAMOUNT.
If I had a stove as a fire box, I'd build a vertical box about 3'X3' and 4 to 6 feet tall. Load it through a front door. I'd duct the firebox chimney into it at the bottom with double wall flue pipe and put a simple slide damper on top of the smoke box. If I wanted to smoke in the winter, I'd double wall the smoke box as well with fiber insulation, unless it was wood, then I wouldn't worry about it. However, in warm weather, keeping the heat down would be a challenge with a big firebox.
Jeremy