Most "bug-out" ideas are by sons of Walter Mitty. Carrying some kind of compact reloading tool wouldn't be hard but carrying enough reloading components to make a difference in a SHTF life is dream land. Far better to carry a small rifle and small handgun with all the ammo you can pack in a sack already filled with food, clothing, axe, etc.
IF I had to run I'd choose a .22 RF for both weapons - a Ruger 10/22 rifle with rugged (iron) sights and a Mk. 3 pistol - along with a compact brick or three of low noise rounds that can kill small to medium size back country food animals pretty well and do it quietly; all without the hassels of trying to reload while living in a dank cave.