02 Honda Civic problem, maybe Catalytic Converter

I’m having a problem with my '02 honda civic. It has been running poorly when cold for the last several months, to the point where when I give it gas the engine doesn’t rev and it doesn’t go anywhere until I let it warm a bit first. Within the last week, the check engine light came on and I took it to a dealer who says that the problem is that the catalytic converter needs to be replaced based on the error code.

I know that replacing the CC is really expensive, so I’d rather not if I can avoid it. It just doesn’t make any sense to me that a bad CC would cause problems when the car is cold but be fine when it’s warm.

More converters get changed unnecessarily than should. The device that checks the converter is the downstream oxygen sensor, past the converter. It compares the oxygen level with the reading from the upstrem oxygen sensor, in front of the converter, and of the change doesn’t fall within specified parameters it trips a CEL saying the converter is operating at low eficiency. The weakness is that a bad sensor reading can trip the same flag. The only way to really tell for certain is to put the readings on a scope. But few places do that. Most see the caode, change the converter, and then if the customer returns they check the readings.

Going to a reputable independant dealer could save you tons of money on this. Assuming they read the same code(s), ask them specifically to read the sensor traces and verify that it’s the converter before changing it. Even if you do happen to need one, an independant can get you an aftermarket converter for hundreds less than the dealer will charge.

Would an O2 sensor be more likely to cause the problem of running badly when cold than a Catalytic Converter? Or is that most likely a whole other problem?

Neither the cat converter nor the O2 sensors could cause the warmup drivability problem you have.
The converter related computer code is a red herring. A side effect, not the problem.
It’s running too lean when cold.
How many miles on the car?

Get these things tested:
coolant temp sensor, intake air temp sensor, MAF sensor, fuel pressure.
it might be a small vacuum leak or a clogged fuel filter
a bottle of Techron in the gas tank might clean dirty fuel injectors