You can buy "STAYBRITE 8" solder and the appropriate flux at a local A/C supply house. The solder is fairly low temp and has an 1800 psi tensile strength. It's basically a soft solder used as a much better replacement for the old 50/50 stuff. Use the flux that comes in a paste, rather than liquid form, and use it sparingly. Tin the barrel with a little solder and do the same with the bottom of the sight. Then clamp the two snugly and apply a little heat. I've done ribs and forend loops on SxS's using this method and had no problems with losing any of the existing blue. The heat required is low enough that there is no problem with changing metal color either.
Solder prices are through the roof nowdays, so if you know anyone in the A/C business, you might ask them for a little, rather than buy a full roll.
Luck,
Jim
You know what? It just dawned on me. Send me an address, I'll mail you a few inches of solder. You get the flux locally. The stuff you need looks similar to petroleum jelly. Don't use the white paste flux used more for brazing. It won't work well and may very well take off the bluing. I've never tried it on a gun.