For the leads, I would tend to want to use shielded twisted pair for each lead. That would make them much worse antennas (a good thing). The shield (i.e. the "drain wire") would then be connected to chassis ground, near the input to the box, and connected to nothing on the sensor end. And the two internal wires in the twisted pair would be signal and signal ground, or a differential pair. Either way, they would ONLY connect at the first active amplifier, and NOT to the chassis at the input connector, for example. You would keep them twisted inside the unit, too, ALL the way to the input resistor(s).
If you are getting a lot of 50 Hz, then there is probably space between: 1) the two conductors in each (or at least one) of the input leads, and probably also between 2) the wires of the AC mains pair that connects to the transformer, and between 3) the wires in the pairs from the transformer secondaries. Those pairs must ALL be tightly twisted! And if one of the AC wires runs to a power switch, then always run the other one there, too, and keep them twisted ALL the way to the switch (and fuse) and back. But first try either tightly twisting the input pairs (or use shielded twisted pairs), both inside the box AND outside the box, and see if that might be good enough.