Regular 60/40 or 50/50 lead/tin general purpose solder works fine and was used for a few centurys w/o much problem. I've used 60/40 and regular NoCorrode(sp?) paste flux to re-rib a hundred or so cartridge SxS shotguns and rifles and reattach loose ribs and have yet to have a complaint.
I don't like using the the so-called acid flux mixtures (they are really metalic chlorides usually). The heavy after-rust possible from them if they are not completely removed is too great a risk inside the voids on SxS's. It is really agressive and difficult to remove.
It does work great as a flux, but with clean metal and procedures, a regular non-corrosion paste flux works just as well w/o any thought or worry about a future problem.
It's the soldering job you do not a magic solder or flux that does it for you.
Clean the metal,,flux and tin the surfaces,,re-flux lightly & clamp the pieces together by one method or another and sweat solder the parts together.
Don't over heat,,don't burn the flux.
You can add a touch of extra solder when the parts are up to to temp and the solder flows, but generally they don't need much if fitted up well which is part of the 'secret' to a strong soft solder job.
Soldering isn't a gap filler.
The silver bearing soft solders so common now in this greenie world (95/5 I think they are,,tin/silver) are stronger in many cases than the lead/tin compounds,,I don't see the need for any extra strength over the lead/tin solder in this application but such things do draw the interest of some.
Also ,on old (re)work or restoration I still prefer the lead/tin as any thin line of solder showing at a joint will darken to a dark gray almost black color.
The silver/tin soft solders are called "stay-bright' for a reason. They do just that. I imagine any joint line from them could be colored in some way,,but it's just another step and a touch up at that.
Just some thoughts.