If you do carry a spare cable and don't carry a cable cutting tool, cut off the crimped-on end caps before you leave or you won't be able to replace the cable in the field. Then you have to deal with fraying cable ends.

But I agree with the others that after a close inspection before the trip (not so easy with some shifters), carrying a spare is not needed.

It doesn't sound like your route goes through Medora ND, but Dakota Cyclery is an excellent bike shop.