Even with an hydraulic helm system, the engine will still have a power assisted steering, and it's associated cooler. The photos are of the front of the engine, the cooler is at the rear. The plug you're removing is the digital temperature input to the ECU. The alarm you're hearing is not an overheat, it's the ECU telling you it has no signal from the temperature sensor....
Just had another look at the photos, and text. Which wire/s are you disconnecting? The single tan wire (stbd side of thermostat housing) is the sender for the temp gauge on the dash, nothing to do with an alarm, it's ONLY for the gauge. If you unplug it, all that will happen is the gauge will stop working (if you have the older analogue gauges). The plug on the port side of the thermostat housing is the digital temp sender.