I'd also include three feet of the heaviest weed whacker line you can find that will still fit down your bore. Coil itself up on itself and keep as part of your permanent pack contents. Tape over the muzzle should protect you most of the time, but in the event you have an obstructed muzzle, your fishing line won't push through the blockage.
I've carried a coil of trimmer line for years and have never needed it, but I'll continue to carry it.
This is a great idea. Although I only take tape. If mules, or lamas, or goats were involved I'd do this and a bore snake.