Replacing the railing on an old rock retaining wall
Cut the existing fence out in pieces, preserving as many of its original vertical support posts as you can.  Instead of solid 6x6 lumber, use four pieces of 2x4 lumber in a square, and secure them tightly to the original posts.  You might also be able to design a special pentagonal support this way that would work well in the middle corner of your wall.

Or if the original support posts are hollow below grade (which is a long shot), cut them off flush, and embed new threaded rod inside them with epoxy.

Anther option is to accept that you're going to damage the wall when putting in new fasteners, and also plan to add a new cap layer to the wall that would cover up that damage.  Avoid using high impact hammering, try to find a bit that can grind instead, and use plenty of water to wash it out while drilling.