Back home again and able to comment further, but not sure how helpful this is.
My aforementioned M&W Micro 2000s & Microstat were originally supplied with a NiCad stack of either 3 or 4 button cells depending upon the model.
The folk who now maintain them, and supply spares, sell NiMh as a direct replacement, and assure me that everything will be fine.
Up to press, that appears to be the case.
Previously I've made sure that I only charge NiMh batteries in a NiMh charger, though I do sometimes charge NiCads in a more modern NiMh charger.
They, are all larger cylindrical NiCads from AAA to D, rather than button cells.
One of my early NiMh chargers actually has a switch to set the charging schedule depending on the battery technology; the later ones claim to work with either.
Battery University does suggest that NiMh in a NiCad charger can overheat, but I don't know how much this applies to the smaller button cells, which will have a very low trickle charge rate, and originally be designed for it.
https://batteryuniversity.com/article/bu-408-charging-nickel-metal-hydride
Since NiCads are all but unavailable in the size you need due to H&S regs re the Cadmium part (a bit like silver solder), it's all a bit of a moot point
I can only suggest a suck it and see approach and try a NiMh stack, but monitor how the flash gun charges the cells, with volt & ammeters as well as a non contact thermometer.
You can measure the mAh charge rate, and knowing the capacity, should get a good idea of the charge time(ish)
If need be, one could always use a timer to prevent over charging; I suspect leaving them on permanent charge would be bad for either technology.
Bill