As Dabac mentioned, it's not just a matter of sliding on, but having a secure fit equivalent to what a press fit would produce. The conical race and tapered compression ring do this and are key to the threadless design.

An alternate "poor man's" method if the OP wants to save his headset would be to carefully ream the cup to the closest fit which still allows it to slide on the fork. Then using a half round or rat-tail file, carefully filing an angle into the top corner to accept an O-ring which will be crushed into it. You want something that goes deeper than 45°, so that most of the wedging force will be radial vs. axial. The O-ring needs to be thick enough that it cannot be pressed entirely into the recess. This provides the poor man's compression ring effect and press fit analog needed for the headset to work.