The first step is to wash away any wax, because that gets in the way of the sandpapering. You can remove wax with naphtha or mineral spirits. Allow to dry; it will then look even worse. I had a lot of big paint drips, which I chipped off with a dull edged tool (butter knife, dental scaler) . Then to the true grit! Use 320 sandpaper, like Klingspor gold, at least use a better grade than plain aluminum oxide on A paper. The more expensive paper stays sharp longer, does not clog as readily. The 320 is fast cutting, so be super-careful at edges, you will sand right through to the wood unless you use the utmost care. You can mask off to within 1/16" of edges with tape to be safe, sand one side at a time, shifting the tape in between. Wipe or vacuum the dust from the work when it begins to build up. (This is messy, you may want to work someplace besides your front room, and perhaps wear a light dust mask) Watch what you're doing, don't sand through, and get the alligatored surface down just to where it looks more like a tracery of spiderweb lines, but with no texture. Wet with mineral spirits to rinse off the embedded dust. If you stopped just then and applied a new top-coat of finish, that is what your article would look like, wet with solvent.
The last step, seen in the second picture, is repolishing with shellac. If you noticed that the dust/slurry went from grey to tan, your organ was originally polished with an unbleached amber or garnet shellac. If the last of the slurry was white, then you had an organ polished with refined clear shellac. Different makers used different shellacs on different models. And the finished color depends on the type of wood and the color of the stain, but also the color of the finish. I generally use some garnet shellac on the first coats wherever walnut wood is used. I buy the shellac in dry flake form and dissolve it in alcohol. Fresh shellac is the best shellac!
I apply the shellac with a pad/rubber/"tampon"(french term!) made from very fine cotton cloth (lint free, nothing knit) with a core filler of cotton (all or part of a cotton sneaker-sock is great, knit material is acceptable, just as long as it's clean) Wet the filler with alcohol. Wrap it with the cotton outer cloth. Make a sort of square, flat ball. Pound it into your palm to set the shape; adjust the parts to remove creases and wrinkles, it must be smooth with no rills or ridges, or the finish will not go on smoothly!
I put the shellac (a thin cut, no heavier than 1 1/2lb) on the pad by dabbing with an almost-dry brush out of the jar of shellac. There's no way for me here to transmit to you my exact technique, but it involves wiping on layers of shellac that are instant-drying because they are microscopically thin. The trick is to not have lap marks. This is a function of how much shellac is on the pad (very little dab), where it is on the pad (center!) and how you set the pad down in motion, and how/when you lift it. The last bit is an acquired feel. I wipe and skip a row, then after every other row has had one pass, then fill in. For subsequent coats, always shift 1/2 row aside, so you are never wiping down the same exact path!
Below you will see what I call "the last Mason & Hamlin" built May, 1918, in mahogany (yes real stuff, I know how to tell the difference) in a rosewood finish, with real tusk ivory keys and several special stops. This organ was crackled all over, and was completely re-polished with my technique. What a little beauty; it moved to NYC and became quite famous!