Originally Posted by
sweeks
Flicking the end of the cable before the solder solidifies gets rid of the excess. I use s screwdriver to deliver a little "whack" to the cable end.
And if it chills before the whack, just re-heat with whatever heat source you used to do the soldering. Job best done with excess cable still waiting to be cut off BTW. Securing those tiny wire filaments first leaves a clean end once excess has been parted from the rest.
I've done this for years, the crimp-on ends weren't something I had access to until a couple years ago. Solder & suitable torch? Since grade school days half a century ago.
I do like the look of this -

- but not enough to justify the expense of yet another single-purpose tool at this point.
As posted earlier, lead-free plumbing solder may or may not be silver-bearing.
Even the cheaper tin+antimony alloy costs more than the old lead+tin alloy but ought to still work on bike cables if used with proper flux. One doesn't need silver alloy to do a decent job of it but it does look pretty once you're done.
Any decent hardware store ought to stock suitable products among their plumbing or metalworking products. Look for metal-repair types; solder meant for electrical work likely uses a different flux that doesn't work as well on non-electrical components.
Expect to pay around US$15 for enough to solder maybe 200 cables, more if you're careful about it. If you don't already own a propane or butane torch, look for the cheap grill lighter things -

- with a trigger and long 'neck' and a small, pencil-tip size flame. Those work just as well for smallish metalworking stuff like this.