I've used Fiebing's leather dye on a lot of small wood projects with great results. I haven't tried it on a rifle stock yet, but I'm tempted.
I like using Fiebing's on stocks. I started using it while working part time at a gun shop in the 1990's. The owner bought several dozen various military surplus rifles, and wanted the stocks redone, so he had us do it a certain way. He bought Enfields, Moisin Nagants, some Mausers (though not all German) and a few Garands. We'd take off all the hardware, and strip off the old oil and any finish, down to the wood. It was amazing how the wood would bounce back after so many decades. We'd apply a damp wash rag and an iron to any dents to get the wood to lift the dents in the stocks out. Then we'd "de-whisker" the raised grain with 4-0 steel wool. This would be followed the Fiebing's in light or medium brown, and then an application of boiled linseed oil with 4-0 steel wool. The stocks would get a coat of BLO for five days in a row, then a coat per week for the next three weeks. The rifles were then reassembled and sold. Wow some of them had some pretty good wood. The owner had the metal parkerized. The stuff wasn't sold as "authentic" just pretty, vintage WWII, and useable.
I'd do the same pretty much for Bess stocks needing an overhaul, sometimes because whatever finish had been applied was flaking off, or somebody used an oil that darkened over time, etc. I've used it on rifle stock too for my flinters and caplocks, BUT..., I like very plain stocks on a lot of my gear (knives and hawks too), and that's also what you get on a Bess for wood. They look great when done but they don't have much figure..., so there's no harm nor disadvantage to using Fiebings on them. If I had a high grade curly maple stock I'd be looking at using Aqua Fortis.
In fact I just got a bottle of Laurel Mountain AQ last April for use on some very curly maple to be used as knife handles. (Winter Projects) :grin:
Minwax is good on pine boxes, and on pine stools, followed by some Bear or Thompson's Water Seal. Looks good but not authentic (any stool for somebody under the rank of Serjeant is not correct, but many of the lads are more long in the tooth than me and simply cannot sit long upon the ground)
LD