How to test high voltage Zener Diodes with multimeter?
Yes. It is possible to measure the conducting voltage of a zener diode. You simply have to have a current limited power supply with a larger voltage than the zener. However, there are a number of precautions to take.

Personal safety

Any voltage above the 40v to 50v ballpark is deemed to be no longer touch safe by most authorities. Have everything at high voltage insulated. Use a switch so you can connect and disconnect the zener diode with no power on the clips.

Power dissipation

Most small zener diodes, 2mm diameter 10mm long ballpark, will safely dissipate 200mW or so. As you don't know the voltage you're going to get, it's important to limit the power your power source can put into the zener.

The 96v + 1k source you've illustrated in your question can source a maximum power of 2.3 watts into a 48v diode. If you measure the forward voltage, then it will be around 1v, and R1 will be dissipating 10 watts. Is it big enough?

If you use a higher voltage, you will need to redo the sums for power dissipation, and choose larger resistor values accordingly.