Ok so here we go.
First off you shouldnt have bought a 99 to fix a 96.. i know they look the same but 96-98 is obd2a and 99-00 is obd2b.
With that being said, youre not screwed or anything.
I wouldnt have taken the motor harness off the engine because its easier to pull with it on really, you should have just unplugged it, unbolted it from the firewall, and pulled it through the firewall. Anyways, not a big deal.
So now, lets see what you have to do to swap it. Because its more than you think.
Your'e gonna need the engine harness and interior harness, yes youre gonna have to pull the dash on both cars as the obd2a and obd2b harness wont work with eachother.
So, swap the cabin harness, engine harness, and sub harness.
Swap the motor out of the 99 into the civic, also use the p2p ecu out of the 99.
Now, that all thats done, it should be fine, but youre definately gonna need to do all that. Its not as simple and just putting the motor into the other car. They also came from factory with different motor so things are a little different.
Im sure theirs ways around swapping all the harness's but i guarentee the motor wont run correctly if you dont. This is the right way to do it and have the motor run perfect.
Good Luck.