I am trying to remove the barrel nut on my barrel to replace it with a new one.  Once I remove the delta ring and the snap ring, will the barrel nut just slide off as well?  or will I need to remove the FSB?

The FSB has to come off and the barrel nut slips off over the muzzle.

I may be posting the obvious...  but I couldn't tell from your post.

Unlike the delta ring, which is held in place with spring pressure and a snap ring, the barrel nut is actually threaded on (CCW torque to loosen).  You'll need an armorer's wrench to get it off (at least without tearing it up).  Neither the Delta ring, nor the barrel nut will come off without removing the front sight tower.

Sorry if I am telling you something you already know, but your post made it sound like you had no experience with how AR barrels are attached.

- AR