Since the cable and amplifier are unbalanced, a tiny current from stray electric field is induced on the high impedance side only and not the ground side thus a difference potential is amplified.
It appears as if the example you show has EMI-type copper foil with adhesive substrate wrapped around the sensor for electrical insulation. The vibrations still couple thru it but the copper shields the electric field around the sensor and bypasses any current induced by your hands touching it.
You need a drain wire soldered to the copper with strain relief like hard vinyl tape or kapton tape.
simulate this circuit – Schematic created using CircuitLab
It is critical that any sharp edges on the sensor does not puncture the adhesive and electrically short itself to the foil for ground guarding.
Then use shielded twisted pair wire with the copper connected to the shield only at the sensor end and chassis ground at the amplifier end or signal ground for best results.
Grounding the copper at both ends may work but not as well.