You were on the right track with the hose, but I certainly understand you don't want a hose laying across the lawn all of the time. What I would suggest is tie into a water line that is not valve controlled possible the one the hose was connected to. Bury a PVC pipe under the lawn. One problem with connecting to a sprinkler zone line is that those lines are not charged with water until the zone valve opens. There would be a time lag while the air in that line was expelled and the cat sprinkler activated. A dedicated line would be fully pressurized at all times so the cat sprinkler would active instantly.