Hello Siu-yu,
i understand that salt water is generally thought of as corrosive to wood, however, i keep thinking of how Venice is built upon timbers submerged in brackish water.
That is excellent that you know that Venice is built first on wood then stone...!!..
Salt water is not corrosive to wood...However, the ocean has had millions of years to evolve many species of "sea worms" and other organisms that take full advantage of the "drift wood" that falls into the ocean. These are the bane of wood sailing vessels, both in tidal and pelagic seas.
When you get the wood into fresh water of into the deep sediment of mineral sea bottom (like under Venice..

) The anaerobic state and minerals will preserve the wood (for the most part) for millenia. Some wood found in such environments (peat bogs for example) will yield some of the finest wood in the world to work. It is extremely stable and be as much as ten thousand years old or older...
most of the DIY walnut stains are water-based recipes (save for one that uses methyl alcohol, which we are not going to try), but was wondering if salt water might also be used as an acceptable stain for wood?
Yes...is the short answer, yet it most likely will produce mineral salt precipitates. These types of "finishes" are natural alternatives to "wood preservatives." So you can use them, but probably not for an overtly aesthetic application. I would encourage experimentation! You may be surprised and like it...
...we would also most likely add borax to the solution as well, following an 100 year old recipe i found in an old homesteading book.
Borax is an excellent choice (and Permie acceptable as a naturally occurring mineral element.) As a nitrate family mineral (aka salt) it has a broad spectrum of ecologically neutral (or less harming) preservative, cleaning agent, and even food preservative in some applications.
I would again encourage some testing and experimentation with the vintage formulas you have found.
we are also considering soaking walnut husks in olive oil to create an oil-based stain..
Olive and related plant based lipids of this type do not "polymerize" when exposed to air as they are "non drying oils." They would only form a gooey and sticky mass in most applications. However a nice "food grade" walnut, tung or
flax oil would work awesomely in such a mix...
Regards,
j