I would say, that your meter is working properly. If you connect a wire to the magnetic pick-up input of your stereo and turn the volume control up, you will hear a strong hum (and maybe damage the loudspeaker). It is the same effect, the unshielded wire is picking the surrounding electrosmog and passing it to the amplifier inside your meter.
If the circuit under test has relative low impedance, a couple of banana wires may work. If the impedance is high, you will introduce hum in the circuit and false the measure.
I have a TRIO vt-106, the input resistance is only 1 M instead of 10 M. It shows 130 mV with an 80 cm wire connected to the input. A shielded probe shows just 6 mV.
The usual procedure to avoid violent movements of the needle is: 1) select a quite high range 2) connect the probe to the circuit under test 3) select the proper range and take the measure 4) select again a high range 5) disconnect the probe from the circuit