Sounds very much like a Bowden control cable.
That's the type as used on bicycles, motorcycles, cars etc, that have a
multi-strand inner cable with a nipple on the end.
The method you describe for putting on a new nipple (ball) is OK, but
you didn't mention if the nipple had a hollow cone, or double-diameter
made into it. If it's only got a straight hole, I wouldn't expect that
to last long. The larger diameter or cone is where the cable strands can
be spread out into, and optionally a steel "splinter" can be also placed
centrally, before it's all soldered. Using the proper solder, or maybe
silver solder, and cleanliness helps a lot.

Jordan

Robert Latest wrote:
Hi folks,

I'm having to fix a steel cable (1/8" dia) to a small metal ball (1/4")