I've read a plan where they planed to do this up the side of K2 getting it out of a good percent of the atmosphere (over 28K feet) before it's released. The plan was more elaborate though involving high energy ground based lasers tracking it and flashing H2O to supercritical steam thus providing thrust in addition to its initial kinetic energy. This was push mass in to Lagrangian points not just LEO.
There's not much development around K2 so no one would be bothered by the shock-wave.
Because you're not as concerned with the mass of the projectile you could surround the satellite by some sort of heavy sabot to protect it in atmospheric flight.
The problem I have with this is, do we really want all this stuff up in orbit? There's enough junk up there as it is.
Right. But it is the wrong junk. It is somebody else's junk.