You will need to use the '99-'00 Si harness. The ECU plugs changed slightly (I don't know if just in wire location or physical design) and are sometimes refereed to as OBD-IIa and OBD-IIb. Since you will need to an OBD-IIb Si ECU, you will need the OBD-IIB harness to plug into it.

On the '96+ Civics, the wiring harness connects to the ECU, passes through the firewall on the passanger side and goes directly to the engine ('92-'95 Civic's and '94+ Integra's had a sepearte engine and in-car harnesses). Assuming the engine comes with a complete harness, just leave it on the engine and use that. I believe there are some issues with the 2 being somewhat different (something with an gas tank pressure sensor the '96-'98 Civic's don't have) but I don't know all the specifics as I've never done that swap. I also don't know what kind of issues you will run into with the automatic changeover concerning the wiring differences.