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I think what Conanski is hinting at is that you can dump the air injection if you want. Plenty of guys on here do just that, and I've done it as well on older trucks (my 96 didn't come with it). All you have to do is ditch the air pump and re-route your belt, or replace it with a shorter belt. Then you can run headers without air injection.
The only reason they even make headers with air injection is for places like Kalifornia where you have to have every last nut and bolt in place on the smog equipment to pass inspection.
I have a 94 motorhome that I put headers in. I just welded the air holes closed, as well as the egr. The smog pump seized anyway. As I was taking things out other things started breaking, so it all came out. Seems to run ok.
'96-97 CA-emissions 7.5s did not use AIR injection to the manifolds - just the one air pipe to the inlet side of the catalyst. I'm converting my '95 to '96-97 CA-spec emissions (Mass-air/SEFI) and putting on mid-length headers (with no air fittings) it in the process. The mass-air conversion will also allow more engine tweaks (bump in compression, and mild cam upgrade).
As others have said, you can dump the AIR injection entirely if you want to - it is only there to help with cold-start emissions until the catalyst warms up to operating temperature.
I would not keep it, just more stuff to fail after 30 years. Keeping yours in tip shape, with a high flow catalyst, does more for the air than some old emissions devices that probably barely work.
Keep in mind, you need to remove properly not to have codes.