The sawdust and glue method works very well and I have used that method quite a lot.
The "traditional" glue would be white carpenter's glue, but cyanoacrylate glues (AKA "Super glue") work well for this also. Both are completely reversible.
You may need to mix some colorant into the mix if you want to match the color. Old mahogany will probably be darker than most of what's currently available.
Also, if you go for the super glue method, get some water-thin type from a hobby shop (the typical product has thickeners), and then you would pack the sawdust into the crack then apply the glue in drops. The sawdust will wick the glue. You may also need to spray it with a setting accelerator to finish things off.
BTW, there are several grades and colors of shellac, from deep amber to almost clear. Woodcraft (
www.woodcraft.com) has some good videos that go into the details of the various shellac grades and types.