A lot of 'hardware store' denatured alcohol as well as that sold through places like Lowes, Home Depot etc. is not only alcohol but usually has other solvents added as well. Not good for this purpose, as those "other solvents" may attack the underlying oil finish, even if slowly. Best to get some straight methanol, which is historically what was used for mixing shellac, or if you can find it, anhydrous isopropyl (not typical rubbing alcohol, which is cut with water). I'm pretty sure most luthiers use anhydrous isopropyl now for French polishing as it evaporates even faster than methanol.
This may sound like overkill but that's a darn nice piece.