Yes, basically, for our use in test loads, you can considerate them 0,7 / 0,8V, it's not too much important in this case ..... just use 1N400x serie for currents til 500mA, and 1N540X / BY255 / BY500x serie for high current loads (or, more simple, just build a test load using directly 3A or 5A diodes, they works good for high currents and also better with low currents, so you don't need to build 2 of them

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After all, (but you probably already know this), diodes in the test load are used for simulate a "real laser diode" load type, with its own dropout voltage, so the setting of the load can be done with a load that try to reproduce in the more accurate possible way the dropout of the real laser diode, and in this way you can check if, with that type of load, the driver work good ..... so, you don't need a super-precision in dropout simulation, just to get a value close enough to the laser diode that you want to use .....
Just for give an example, imagine to use a boost drive with a maximum output voltage of 5V ..... if you use it with a red laser diode, it's ok, if you use it with a BR diode with 6V FV, it don't work correctly ..... but if you set up the driver with a pure resistive load, or with a load that don't have a dropout similar as the BR diode, your driver works good during the set up process, and you find it non working correctly only after, when you have already soldered it on the laser diode .....