The really expensive part of space travel, in terms of fuel and energy, is building up the velocity for orbit. I.e., "climbing the gravity well". That part at least is solved with the gun/cannon.
The next most expensive maneuver is changing orbital planes, that is, change the "tilt" of the orbit in respect to earth's axis. It would make sense to build the gun so that the payload ends up in an orbital plane very close to the ISS's. (Or whatever is the intended destination.)
Then, a space tug would only have to adjust height, eccentricity and phase, which are very cheap maneuvers. It might just be economical.