Bi-directional electronic switch for external circuitry
If you are able to convert this 10V/1mA (1) to a bit more mA @ 1V or 2V  you may want to consider using a "photovoltaic relay" or "solid state mosfet relay":


where pins 3 and 4 are the isolated terminals A and B.

You should check the maximum required "trigger forward current" or "the minimum control current" or whatever description that tells you which current you need worst case to turn on the internal LED.  

In my small research I found a few that need about 2 to 5 mA. The G3VM only needs 0.2 mA typical and worst case 3 mA.

(1) It's not clear to me, but it seems this 3V3 regulator mentioned in the comments is such an example.