I'm not sure how important the current measurement actually is. The spark gap will break down at a certain voltage, which of course is something that you need to measure, but from that point, the current will be determined only by the amount of current that is
available . For instance, if straight across the mains, then it would immediately develop into a severe arc, limited only by circuit impedance, until a breaker or fuse goes. This is where CAT ratings come in on DMMs etc.
The magnitude of the spark or arc will determine the magnitude of PCB destruction - from a slightly increased conductance across the gap, through carbonized and unsafe, though to total destruction.
I think you may be able to get more meaningful results by measuring leakage resistance across the spark gaps, before discharge, under various types of contamination, and after discharges of various levels. This is probably more useful information to the manufacturer. There are plenty of cheap high voltage insulation testers available these days that might be helpful.
You can probably do a better job by
dictating the peak discharge current using capacitor(s) slowly charged to known voltage, and using defined high surge current series resistors (
and great care for personal safety!). Using the capacitor voltage when the discharge takes place and the series resistor value, you can then accurately determine the discharge current.
You might be able to detect a small bias in my attitude towards PCB spark gaps - I think they are the spawn of the devil

and a relatively recent 'technical' looking 'fad' which will soon die out again.
Please be sure to evaluate spark gaps with routed slots in the PCB too, rather than just different tinned 'electrode' shapes on uninterrupted PCB. Forcing an air gap between the electrodes is the only way I can see of making them
relatively safe, and mitigate the large change in characteristics after the first discharge due to carbonization of the substrate. Even these need to be evaluated for different degrees of contamination, dust etc.
I hope you are able to get some meaningful results to pass on to your sponsor.