i'd be surprised if the hx uses the same fuel injectors as a DX.
pretty hard to swap an obd2 engine, and still have it pass smog. usually they plug in, and want to see the right VIN number inside the ecu.
Reprogram VIN in OBD2 computer? - Honda-Tech
the VIN includes the hx/dx model, so I don't know if the dealer would even do it for you.
Not saying it can't be done, but.....
Also, finding the ECU for a 97 civic is like dead easy boring. Don't you have a pick a part locally? here they sell for 40 bucks.