It's an older engine. There are going to be more concerns with the engine's ability to efficiently ignite the air/fuel mixture. A new catalytic converter may very well allow your Volvo to pass the smog check IF in fact the current CAT is defective. If not defective, replacing your Volvo's CAT will offer no benefit in terms of passing the smog test or lowering NOx. It is illegal to replace any vehicle's catalytic converter unless a complete and thorough diagnosis is conducted first.
The component we'd first recommend inspecting for proper operation is the EGR valve/system. The EGR valve is responsible for re-circulating a small amount of exhaust gas back into the combustion chamber. This is done to cool down the chamber temperature by producing an inert gas along with the regular fuel mixture. Nitrous Oxides emissions are formed when engine chamber temperatures rise above 2500* F. Keeping the chamber cool reduces NOx emission.
A complete diagnosis would entail what is referred to a the "Fuel Feedback Test". This includes ensuring the oxygen sensors and over one dozen additional emission sensors and solenoids are working properly, your Volvo 940's emissions computer is receiving these signals, the ECU is computing the data properly and sending the correct signals back to, mainly the fuel injectors and other solenoids designed to control fuel delivery, by either increasing or decreasing the amount of fuel entering the intake manifold or combustion chambers.
On OBD I Emission Control System vehicles such as your Volvo 940, the check engine light will not necessarily illuminate when emissions are high or emission components are marginally failing. 1996 and newer OBD II System are much more accurate.
