What is the best way to handle house wiring cables with short sheathing?
I would get some white heat shrink slide it over the conductors and make sure it extends inside the box the 1/4” and at least it’s width past where the sheath was removed.

I have skinned the outer sheath several times in the past. The inspector only asked to verify if it was listed and then asked me to change from the black shrink tubing to match the color of the existing outer sheath. Way cheaper than tyco splices. My jurisdiction allows this others may not.