Silver solder is probably the best method of attaching the steel
cable, the discoloration is the formation of oxides and should be
easily polished off of the surface.
The best way to darken the surface of the steel is probably not heat,
although it can be used to obtain colors ranging from light tan or
straw to a dark blue. The steel must be coated to preserve the oxide
on the surface, it will be susceptable to wear and scratches. A better
method for darkening the surface would be the application of organic
acids in the form of lemon juice, tomato juice, ammonia (kitty litter
that has been dampened by the cat works very well) etc. You should
experiment to find a method that achieves the darkness and hue you
desire. Leaving the surface of the steel in contact with various
clothes, sponges, etc. during the process will allow you to achieve
some patterns, too.
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