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Since you don't need much accuracy, why not just use a simple 1 transistor current sink.The circuit below uses a 2N3904 and 3 resistors. Testing shows that it works down to 0.2 volts. Current was about 1 ma at 0.2 volts, up to about 1.2 ma at 25 volts. If you don't have 5 volts available, just recompute the base bias resistor divider for whatever voltage you do have.