I've always used navel jelly to remove all old bluing and finishes, including the years I co-owned a gunsmith shop. That included for the restoration of a lot of antique firearms and a few original smokepoles that the customers wanted restored to original (re blued, browned or otherwise).
You'll get a much nicer stock by not using stains at all... they block and fill figure and depth in wood. My preference was always 100% pure hand rubbed finishes, and they can be cut as needed if needed. They can also be tinted with products made for them, but... The nicest figured woods is to pre color with aniline dyes if you want to change color, increase depth or highlight figure. They do not plug the wood like stains do. Then follow with as many coats of hand rubbed finish as you can stand to do, the last of them being 100% pure white carnauba wax rubbed in until to get the "shine" you want. Makes them very waterproof... don't forget to also do the barrel channel/inletting.
You can try just staking the front sight (I'm assuming its in a dovetail cut in the barrel). Can be easy done so it doesn't show. Stake only as much as is actually needed to have a tight sight, but that is still drift adjustable. You can overdo it. Staking works on other types of sights as well, on some styles may show though.
HTH. Have fun with your project, and using something you did the hard work for yourself.