Rudder shaft is the vertical pivot for the rudder.I have heard it referred to as a rudder shoe.
I would use new 316 S/S bolts even if the old ones look good. Crevice corrosion is hard to see with the naked eye until it starts to crack. We had a bow eye on a previous boat break under load from the trailer winch. It had looked fine but when it broke we could see where the crevice corrosion had gone about 3/4 of the way through the eye.
Rick, all of the bolts looked brand new. We did replace the SS nylock nuts. They were bedded with epoxy. I had expected them to be corroded after 12 years. Now the rudder shaft had corrosion at the shaft seal location and below. We had to replace it.