EDIT: Thanks to fuggetaboudit, I did some more research, and the pinout, I'd guess, is:
Black = GND
Red = +12V
Yellow = Trip-Point Alarm (see option -04 in the document)
Green = PWM (option -06 in the document)
The document I'm referring to is here. In it, it says a suffix of -09 means:
PWM speed control circuit (option -06 or -56) terminated in a third lead wire (standard = blue) and an open-collector, non-latching, low-pass/high-fail, trip-point alarm circuit (option -04 or -54) terminated in a fourth lead wire (standard = yellow).
Given that your yellow wire acts like an open-collector output and your green wire controls the fan speed depending on an applied voltage, I'd bet this is the correct pinout.
Somewhat relevant: http://www.nidecamerica.com/apps_pwm.htm
I would be very certain that Mark is correct:
Black = GND
Red = +12V
Yellow = Tach Trip-Point Alarm (After checking the Nidec Datasheet)
Green = PWM
Every Nidec fan I've encountered has followed this color scheme, and most common 4-wire PWM fans in desktop computers also use the same color scheme. Empirical evidence, but given your measurements, I'd be willing to bet they're correct.
If you have access to a signal generator, try generating a 25kHz, square-wave, 0-5V signal to the green wire, and seeing how the duty cycle of that signal affects the fan speed.
Even though this has been downvoted a bit, I still think it is a good question because there is a lot of ingenuity in these designs. I have disassembled a fair few of these types of headphones and I can say that there is no single solution.
By far the most often used way is just a bent flat flex - very wide, and very thin. My Logitech H800 uses this technique. Apparently, it is acceptable to have about 2mm-radius bends in this material, probably provided you use very thin copper to avoid cracking.
Another option that I have seen used in my Sennheiser is to have a long serpentine flat flex going all around from one ear to the other. This seems to me like total overkill, and because of the limited available copper I suspect this is only possible with very low current signals (like just driving a headphone coil). This would not be possible in the Logitech example, because that device also carries battery/charging power over the flat flex.
Lastly, in a very cheap headset I have seen just sliding contacts being used. I suspect this to be very low endurance, as exemplified by the short lifetime of that headset.
Best Answer
Although you did not identify the sensor or what kind of wire you are considering, it seems quite unlikely that you will get any voltage drop unless you use very tiny wire.
Assuming the 35mA current rating is for the (undentified) sensor active electronics, regardless of the voltage (3.3V or 5V), any kind of decent cable will provide no significant voltage drop. And there will be no significant current flow in the signal wire because of the (assumed) very high impedance of the destination (a microcontroller or ADC?)
And even if there were some voltage drop, it is unlikely that would significantly affect the operation of the overall system. You could conceivably adjust for whatever detected offset it might cause.
If you want a more solid answer, we need to know: