I don't know if the '96 is the same as my '92 or not. But you are able to remove the seatback foam and cover also without any tools. I recently purchased the Corvette Service Manual and even with that I was confused and had to come back and reread it but here is how it ended up working.
There are two heavy wires running vertically behind the foam. The plastic seatback has four clips and the heavy wire squeezes between the clips. There is a pair of clips in the headrest area - about 8 inches down from the top, and a pair of clips in the lower middle area. To remove, grab the outboard side of the headrest or middle of the seat and push toward the console and at the same time pull it forward. It should be free on one side, then it should easily slip out of the other clip.
Reinstalling can take a couple of tries to get everything in the right place. If this works for you too, please reply to this discussion.
I swapped mine today, I don't think they have ever been out and the driver's side bolster was just beginning to show the slightest wear. The passenger side is like new. While I had everything out I did a good cleaning and conditioning of the leather. I feel like I have a new car. I don't need to worry for a long time about having to have the bolster repaired or replacing the cover.
I had a hard time figuring this out. From the look of a lot of vettes with worn out drivers seats and brand new passenger seats I think this is a little known tip. Let's spread the word!
Mikey
:Twist