You can build a room with carved fortifications in the outside walls and a bridge entrance. Construct the cages inside the room and connect them to a lever outside the room. Get everybody out and close the bridge, then pull the lever. The goblins now roam inside the room and someone will probably already come and shoot them. If not, you can station you archers in front of the fortifications.

Once they are dead you can open the gate, collect drops etc and start over