A friend of mine rode a Cannondale touring bike. His had plastic cable end ferrules that cracked and fell apart. The cable started to explode at the end. If that is what is happening here, you need new outer cable housing, probably for both front and rear. And use good metal ferrules. Might need to replace the bar tape if you replace the cable housing.

For touring, things like replacing cables is good learning experience so you can learn how to fix a bike out on the road.

OOPS, I WROTE THE ABOVE BEFORE i READ THIS:

I usually buy generic cables, not anything special. And I usually buy outer housing in bulk and cut it myself. But as I said above, get good metal ferrules for the ends.

A good pair of cable cutters sold for bicycle purposes is useful. I use one made by Sram. Was not cheap, but good tools rarely are. I got mine at a ebay seller, but I bought it over the counter at their physical store.

Replacing cables in a shifter like you have is something that might not be intuitively obvious, look on you tube for tutorials. Park and some other companies have good tutorials.