How do you build a current source without an amplifier? An emitter/source follower is still an amplifier, because the transistor has a much larger area than in any opamp a relatively low noise one, but still an amplifier. That said, maybe I'm overestimating how low noise the amplifier needs to be. They have 10V to play with, so presumably ~20 Ohm sense resistor, so they need 0.3 nV/rtHz ... that's doable.
Of course, groucho needs less than 2 nA RMS ... which is about 10x better than the SMC11 (minus 0-100 Hz noise even). So that's getting harder.
How about something completely silly. Ping pong between two inductors, when one is connected to the diode you dump the remaining energy in the other into the power supply and then connect it across the supply the other way for a fixed time before switching the inductors. No current is measured at all, the average current delivered is only dependent on the on time while they are charged and the power the laser diode absorbs.