"Audio frequency" = < 20kHz BW, or not many times more than that.
1m of most any kind of cable isn't going to be more than ~300pF, or more than 26kohms reactance (or not many times below that).
So, if you current source is much better than 26kohms, you're wasting your time -- or alternately, if the sensor can't tolerate under 26kohms of compliance or crosstalk. (Which means, for example, a Howland CCS built with 1M 5% resistors will still have a worst case good enough for present purposes, if I'm estimating that right.)
What is this, current bias for a voltage on the sensor?
Tim