[Zeke]

Generally the main source of squeaks are the existing nails. It's a lot of work, but you could pull them using a couple of non destructive techniques or driving them way deeper with a skinny nail set and companion nailing.

I myself might not want to depend on air nailing with out other measures taken. Listen to Greg but unfortunately he didn't see that you can't get to the underside. @oldE has a good idea too. I would do at least some of that or do all of that in a pattern so it looks like it was always pegged.

There are "finish" screws that are set with a drill/driver. The head is half the size but they will hold. You can predrill only the tread and use wood glue slightly thinned in each hole before sending the screw. Give it a minute to get to the stringer.