But if there's a voltmeter and no battery pack, how can I assume electrolysis and not galvanic?
I think this is a galvanic cell, not an electrolytic cell. A voltmeter does not provide energy; rather, it measures energy. A battery is what would provide an external source of energy, and the question does not allude to a battery. So, energy is being generated but not from a battery; therefore, I would conclude that electrical energy is being generated
by the cell, so the cell is galvanic. In this case then, the zinc discs are oxidised and therefore are the anodes, i.e. the negative electrodes of the galvanic cell. The negative terminal of the voltmeter needs to be connected to a negative electrode, meaning the answer is Zn.
EDIT: Also, the fact that soaked filter paper was used to connect the discs suggests that the cell is galvanic.