IMO, I'll say, do not use aqua fortis on walnut. Also, do not use lye water on walnut.
Both of these will darken the surface so much that they will be nearly black in color. All of the grain pattern will also be obliterated leaving the appearance a drab, uninteresting stock.
I'll also say, walnut is usually best left unstained with any type of stain. Although once sanded it will look quite light in color, it will instantly become the dark, rich color people think of when they think of walnut.
After you've sanded off all of the factory staining, find a bright light or better yet, go outside if it is sunny, taking a wet rag with you.
Wet the surface of the wood and take a good look at the results. It will immediately darken and the color and grain pattern you see is exactly the way it will look when you apply a finishing oil. Of course, when the water evaporates the look will return to the lighter color I mentioned. Because the oil you apply to finish the wood doesn't evaporate, that won't happen to the finished gun.
Would I ever "stain" a piece of walnut? The answer is yes but only if there was some very light colored wood showing after I wetted the surface with water. Sometimes, a walnut stock will have some light colored sap-wood in it. If this is present then go ahead and stain the area to get it to match the surrounding wood. Do NOT use an oil based stain like Minwax. It really doesn't stain the wood. Instead, it is like the factory finishes which have all of the color in the finish, kinda like paint. These oil based stains can hide some of the beautiful wood grain patterns.
The best stains to use are the water based, or the alcohol based stains like Birchwood Casey Walnut or Laurel Mountain produces.
While I'm writing, here's another bit of advice. Walnut is a very open grain wood and after sanding it, it needs to be whiskered to keep the grain from rising. To do this, dampen the surface of the wood before you do any staining and let it dry. Once it dry's, small whiskers of wood grain will stand up making the surface very rough. Rub your hand along the stock from front to back and then from back to front. In one direction it will feel rather smooth. In the other direction it will feel very rough.
Use a new piece of 180 or 220 grit and VERY lightly, sand in the direction that felt rough. This will usually be needed at least twice to get rid of all of the whiskers.