Remember, HC is just unburned fuel. Given the inherent combustion properties of internal combustion engines there's going to be some HC but a bad O2 sensor will make it difficult for the EFI to properly adjust itself. Still, the system expects to work with a functioning cat and the computer's tables are set up to give the tailpipe-out values required based on the cat being in the system. For a DD there is little to no advantage to not having a cat in the system so you might as well do it.
I've had excellent results with universal cats (Catco, for example) and I see no advantage to paying the big bucks for a factory replacement. I'm guessing that yours is a 3-way (1 HC/CO brick and 1 NoX brick) but I don't know if your vehicle has air injection between the bricks (some do and some don't). Either way, there are universal cats with the fittings you'll need.
FYI - the advantage of the factory-style cats is that they will light off quicker. While nice (environmentally) as a practical matter I don't think it matters much. The OEM's jump thru a lot of hoops to meet the cold start requirements but you certainly can take your vehicle in for testing with a warm system.
Dan

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