Personally, I just swapped out the stock cat for a 3" CarSound Magnaflow cat,which is supposed to get a little bit better flow than stock, but still be OBDII/emissions compliant. When I 1st had it installed last month, the SES light was going off, but it was intermittant, and I think it might've only occurred when I would drive hard, and push more exhaust past the O2 sensor than the new cat was able to clean up.
I don't know how NY plans on testing emissions, now that the entire state will do E-check, not just the city, so instead of worrying about my SES light chances, I had the code programmed out.

The following is how NY plans to do their OBDII inspection:
NYSDMV said:
How will the inspector conduct the new emissions inspection?
The inspector will complete the same low-enhanced emissions inspection that is currently required for the Upstate Area. To conduct the additional test of the OBDII, the inspector will use the OBDII cable to connect the NYVIP equipment to the OBDII diagnostic link connector (DLC) on the vehicle.
A vehicle will fail the OBDII test if:
The DLC on the vehicle is broken or gone.
The OBDII malfunction indicator light (MIL) on the vehicle does not illuminate when the ignition is set to the ON position and the engine is not in operation.
The MIL remains illuminated when the engine is in operation.
The OBDII readiness monitors on the vehicle report that the OBDII system is not ready for the test.
Myonly worry is that this new tool that the DMV is making inspection stations purchase, does more than read for a code, but reads if a code is actually
supposed to be triggered. If so, I'll be beat, which is why I hung onto my stock cat.
A sound aspect changes with no cat as well. You will get a more raspy sound with no cat, unless you have a free-flowing system that incorporates enough dampening (resonator/etc.) to overcome the increased amount of frequencies being passed through.