With the output side series switch the OP may be justifiably nervous about the instantaneous higher than rated voltage at the time of switch on. These can cause a current spike outside the safe operating range every time the load is switched on though not a problem usually for a filament bulb it can be a problem for an LED and certainly for a laser diode. If there is stray or unintended capacitance before the switch there may be more energy waiting to discharge repeatedly through the LED than is good for it.
The shunt switch to turn off the laser diode is used in sensitive applications and can be designed to drop the voltage to just below the operating voltage of the load for fast response (though even a low voltage will cause a little conduction and light with an LED, almost no laser action is achieved before the threshold current is reached). The shunt method obviously does consume the full load current at all times but in some situations this can be a good thing if you want your power supply to see a constant load, in a simple illumination scenario it is just wasted energy.
I would suggest that the sense pin of the current regulator be controlled. If this pin is driven to ground the regulator output voltage will be limited to 1.2V and through the shunt resistor it is unlikely to be able to pass much current through the LED that is held way below the rated forward voltage. A resistor (say 1 kOhm) to replace the sense terminal link and a open collector/drain output to pull it to ground.
Here is a thread that has gone through all the same iterations as the answers to this SEE question. I just found it using Google image search with the following search phrase lm317 current source switched.
They link to an image of a circuit that looks just like what I was suggesting. It was about the third image in the thread if the direct link does not work.
There are a number of regulators with a shutdown pin that may be even better suited to the task at hand. Parts such as LM2941, LT3022 and UCC281 may be worth checking out.