Sensor cable shielding with wall wart powered acquisition board

[_joost_]

I have a data acquisition board which is powered by a 5V wall wart. It has a single input connected to a sensor on 6 to 12meter length cable. The signal cable is a shielded twisted pair and besides the signal itself carries also power (3.3v) and ground for the sensor.

There is no ground terminal at the PSU, nor at the acquisition board nor sensor. Normally I would connect the sensor cable shield to instrumentation ground at the board terminal but there is no such opportunity here. There is considerable 60Hz in my input signal and I can filter out a considerable amount as my frequency range of interest is higher than 60Hz. However, I would like to do the best possible and somehow get that shield active. What are my options?  Get a wall wart with grounding (hard to get and expensive)? Add a grounding terminal at the board and let customer find a ground connection (impossible for consumer applications I think)?   Or is this the best I can do?