What you're paying for in those expensive probes is calibration (and very small quantity production). But you're capable of doing the calibration, so no need to pay. The issue of noise in the CCS comes down to the sense resistor. Make the voltage across that large enough and noise from the voltage reference barely matters. Obviously, as you make the sense resistor larger, it dissipates more power, and in heating, changes its value. But you only need to drive 1mA, and if you used a 1k resistor, it would only dissipate 1mW. A close tolerance wirewound resistor would be perfectly adequate. Perhaps not a metal foil because they're so small and the temperature rise would be greater. After that, an ADR1399 would produce a stable 6-7V that could be attenuated to 1V and compared by an OPA1641 op-amp to the 1V developed by the 1k sense resistor. That would be a handful of components that would fit in a matchbox. Lead-acid batteries are big, heavy, gently drift down in voltage, and need recharging. The 3458A probably derives its CCS reference from its main LTZ1000 reference.