Fiebings black leather oil-based dye is what Stew-Mac sells, I use their dyes for my leatherwork and I use the black oil-based dye for dying ebony fingerboards and bridges as well. The color has been stable for about 18 years so far on the oldest pieces I've dyed.
Be sure to get ALL of the finish off or it won't take the dye evenly.
Stay away from linseed oil unless you want to re-oil it every year forever. Tung oil would be better, better still may be Tru-Oil.
The linseed oil process for gunstocks goes like this:
Rub linseed oil in once a day for a week
then once a week for a month
then once a month for a year
then once a year for life.
(along with guitar making and leatherwork I do occasional gunsmithing for myself.)
Stick with a polymerized oil product, like polymerized Tung oil or tru-oil. It will harden and give you a more durable finish and won't require the attention that linseed oil does. I finished an acoustic guitar in Tru-oil rather than lacquer and it's held up very well. Has a nice feel too.
BTW, once you get that finish off there's no telling what will be under it...once you dye it you may want to paint it again

and if you want to maintain your sanity buy some good paint stripper and unless there's Fullerplast under it all of the finish will come off.