I have had several rifles brought to me with up to 4 mags of pellets stuck down the bore. What I use to remove them in 177 is 5No, 100mm lengths of 4mm bright bar. Using these, the first one can be inserted into the bore and hammered flush with the end of the barrel and then the next one placed end for end with the one in the barrel and then hammered and so on. Using this bar, if the first one has a square end with a very small chamfer on it there is no chance of damaging the rifling due to the small amount of clearance between the rod and the bore. Being only 100mm long the rod can be hammered without bending. I assume the same would work with a 22 barrel using 5mm bar.