It would be entirely dependent on the trajectory of your projectile, and velocity, mass, density of all involved bodies.

Charon is so closely tied to Pluto that disrupting its path would also disrupt Pluto’s path. So it wouldn’t knock it out of orbit of Pluto, but it would probably make the whole system wobble for a while.

Seems to me that the mass and movement energy of Pluto and its moons are a closed system that orbits the sun, so any such system’s total mass and movement will not materially change at all relative to the sun if any of its component bodies collide with each other in any way unless some other external energy is added to the system.