How to reinstall defrost system

Chances are the mechanic only disconnected the heater hoses to the leaky heater core, meaning hooking that back up will only cause it to leak again. Replacing a heater core is no easy task, most of the time it involves removing the dash board to gain access to it. Try looking up "how to" videos on Youtube for your make and model to see what is involved. Once a new heater core is installed you then have to install new coolant and bleed system. The other part of the defrost system is the AC evap coil, which is also mounted in the heater core box (aka HVAC box) along side the heater core. The AC coil provides the cold for the AC as well as dehumidifies the air for the defroster. When on defrost mode, both heater core and AC coil are working. As you mention "fumes", I assume you also mean the AC coil was leaking? That is more involved to replace. If you have the dash out, I would check operation of both AC coil and heater core, and replace both if defective. Neither job is for a beginner, and the AC coil would require evacuating and recovering the refrigerant. I'd find a mechanic or shop that can service AC as well as handle the heater core. It can take 4 to 8 hours shop time to do a heater core due to removing the dash, so costs are going to be in the several hundred dollar range. Again, consult as many how to vids to get an idea of how involved job is and whether you would want to DIY.