I replaced the second cat and the whole remainder of the exhaust system (known as the "cat-back" apparently not because of some sort of feline spinal column resemblance, but because it's everything from the Catalytic converter Back
I didn't delete the second cat because it's contrary to PA state law, and also because I'm kind of a hippy and don't really like the idea of making my car pollute more, even if maybe I could get away with it. I replaced it because the aftermarket one allows greater air flow, which seemed like a reasonable compromise.
I wanted to delete the muffler, because my hippy ways don't stretch to noise pollution, particularly since the loudest Sonic is still quieter than the many Harleys that pass by my window every night, and because that would increase exhaust flow. But again I ran up against PA law. A nit picky reading suggests that I could remove the muffler and claim that the resonator was a "muffler like device" and still fall within the limits, but I felt it a better bet to go with the stricter interpretation and just put a higher flow muffler in and delete the resonator instead.
After driving around for a bit, particularly on long journeys, I'm going to try putting the resonator back in. It seems that part isn't really very constrictive at all, and that the particular noise leaving it out generates is very wearing. It also looks like the consensus is that the stock resonator will be a good choice, rather than ordering something aftermarket. So it should be a simple cut and flange operation, at least if (as I seem to recall) the two pipe ends are in a straight line from each other.