Tim,
About 8 years ago I had to make up a 'custom' water connection for a heating system in our house (not possible to buy the right thing), and eventually I found a short length of stainless steel pipe (which I think came from a shower unit – definitely not chromed steel, and not magnetic). I eventually silver soldered this to a brass nipple at each end to make the connections, using easy-flow flux. (I checked it for magnetism because like you I was anxious about its provenance before soldering, eventually I had no choice but to get on with it)
It is still in use, and has water at a continuous pressure of around 3 to 4 bar in it. It is part of a heating system, and the water is cycled from hot to cold on an almost daily basis.
I did not have any old solder on the parts – the pipe was 'salvaged', but clean, and the nipples were new brass.
I would have photographed it to show you, but now it it is not possible to remove it without draining a lot of water, and I can't get a shot in place. I hope this is some reassurance.