If I remember correctly there are some slots or fins on the rear side of the large disc, just behind the pulleys. I stuck a large flatblade screwdriver in between the disc and the alternator, put it on the ground, with my foot on the screwdriver, and broke it loose.
--
Bruce S. near D.C.

I'm a little confused by your question "...How do I keep the shaft from turning to remove the nut in order to take off the pulley for the belts?..."

If you're asking:

1) ... because you think that this is how you remove the accessory belts in order to remove the alternator,...

...then this is wrong. You remove the belts by first loosening the nut on the adjuster.

2) ... because you think that the replacement alternator will not come with its own pulley,...

...then you might be right, but it might still be unnecessary. Some reman alternators come with their own pulley, and some don't. But the shop where you buy it should have the equipment to swap the pulley, as most d-i-y's don't have the necessary tools.

regards,
Ken

An air impact wrench makes it easy but any shop will remove it for you, which of course, is even
easier. They made need to swap yours onto the new one.

Next can buy a Vise-Grip chain wrench. It's useful for other things.
Otherwise try a strong C-clamp with a wide thick strip of leather belt to protect the sheaves.

Phil