Commercial source for Oxalic acid cleaners is the well known OxyClean. Very easily found everywhere
OxiClean - Around The House
Home Depot should have had some sort of wood cleaner/bleaching agent for outdoor wood decks.
BTW - hate to break this to you, but you'll never get the nice blond Beechwood color in the furniture you show in your photos from those Bulgy stocks
After OxyClean and Shellac application