I have in mind a pure theoretical clue, but I doubt it will work in real life. Suppose I connect the led to the supply without anything else, and measure voltage and current used. This allow me to calculate the "equivalent resistor" of the led. After I connect a P channel mosfet on high side with the calculate resistor to ground and the gate in parallel with the switching N mosfet. In this way the load seen by the PS should be constant.
Anyway I really doubt that will work, and even if is working, will be a waste of power and money. A dimmable PS is the right way to go!
Ciao, Ale