I've never done this on a Volvo but I also own an '86 Pontiac 6000 STE. About 2 yrs ago I bypassed the heater core by running a hose from the water pump to the engine inlet. All you need to do is find where the hoses go into the firewall, disconnect them from the core and then connect them together suitably. DO NOT just clamp them off. Antifreeze needs to circulate and flow briskly and if you clamp them off and drive it will probably retard the efficient flow. It should not hurt the engine or cause overheating or even throw a check engine light (not sure about this last one on a Volvo though), because cooling of the engine is automatic through the electic fan and thermomechanical thermostat. The thermostat will just open slightly more to let more coolant through and the fan may come on slightly more but you probaly won't even notice. Temp on gauge in instrument cluster should stay exactly the same.

I would reccommend using a garden hose to flush out the heater core with water (on a gentle flow so you don't spray it all through the cabin) instead of just blowing through it with your lungs. Using just air will still leave antifreeze residue inside the core which may leave a smell in the car if you don't take out the core right away. If you still want you can blow out the water with you lungs and whatever is left inside will, eventually, if the ends are left open in the engine bay, evaporate.

I have never replaced the heater core in my Pontiac and continue to drive it this way to this day. But then, I live in Orlando.