Legend

I am building my man cave in my garage. So similar things. Heat, air etc. I agree with above do those individual(space heater and window AC) or separate ducting. Make sure you seal the door. Edges in the moulding and one of those runners at the bottom. Your door will be difficult to close but so be it. I would use wood paneling on the walls and seal the edges with appropriate sealer. Drywall will eventually absorb smoke. Of course keep anything cloth out of there. A small purifier and more important is an exhaust.