I would wrap the lower part in something, plastic foil is probably best because it is slightly elastic and can be stuck together to be tight. You can try lightly oiling the inside of the plastic wrap, so that it might not stick to the cake itself too much and possibly rip off some of the surface. Make sure the cake has fully cooled first.
Then drop or spread the glaze on top, let it set, then cut it away using a knife or spatula, then remove the plastic. If the glaze is soft enough, you should be able to pull it off by simply removing the plastic. If the glaze is very gelatinous, be careful not to tear it during the removal.
If you don't want to have to pull anything off the cake, you could make a thick paper or thin cardboard 'collar', like a cat's medical collar preventing him from licking and biting himself. The narrow opening should be at the top just where you want the frosting to end, taped together there. Make sure is tight enough that no glaze could leak between cake and collar (although a tiny bit of leakage is probably fairly easy to clean up later).