How do I remove the stair treads from under the stair skirt in order to replace just the tread?
The skirt board will be difficult to keep intact by removing it. In an older house, the treads will be face nailed through the top surface, most likely in 3 different rows, 1 at each edge and a row in the middle. The best route to take is to split the tread lengthways to reduce it to narrower widths to pull smaller pieces from around the nails that are holding it in place. There is a strong chance there will be a few nails going into the riser as well, split the tread there first and release those nails, and pull them out. Split the tread next where the next line of nails are and remove that one and its nails.
Do this until you get about 1 1/2&quot; from the riser going up, you may have noticed by now that there are nails going into the back edge of the tread. Carefully pry the last piece off and rotate it out of the pocket left by the notched skirt board. You may be able to back these nails out with a hammer, but you may be able to cut them off and set the remaining &quot;nub&quot; below the surface with a nail set. This should cleaned down to the bare wood so the new tread will be glued to this, and the left over nail shanks will get in the way.
Another method to use, which is a blend of what I described above and another technique is after the nails in the riser at the front of the tread are found and removed, locate all the nails, or at least some of them, and using a nailset with the end, the same size as the nail holes, (most nailsets come in 3 different sizes) drive the nailset into the spot where the nails are, setting them deep, very deep... all the way through the tread deep, deep enough to split the tread in the way I described above but not using chisels or prybars, although they may be handy here too. Remove the split wood as it comes loose.