Those are "trigger" shifters. "Thumbies" are friction shifters like downtube levers, but turned horizontal to mount on the handlebars.

On my triggers, I undo a couple small screws to remove the cover, allows access to remove the old cable and insert the new one is easy.

What *IS* ridiculously difficult, is Gripshifts. Feeding in a cable that has a cut end is super hard because the cable must make a relatively tight 90 degree turn, and the sharp cable end hangs up on the plastic tube halfway in. Trying to rotate the cable didn't work. Much cursing. Perhaps a new cable with the melted steel ball still on the end, would feed better.