I did the same swap.. here's the diff. The "HX" chassis has a 5 or 7 wire primary 02 sensor, and lacks a secondary 02 sensor. I tried to rewire the "HX" engine harness.. but spent way to much time and couldn't get it to work.
Here is the simple way to complete your wiring issue. Purchase a 96' Civic "DX" engine harness, it has the plugs for both Primary and secondary 02 sensors. Your 97' LS computer will fit along with all your other conections. It will save you a ton of time.
You might want to double check the Dist. wiring plugs, they might need changed. I'm not sure what plugs were on mine from the start.