I don't think you can charge most modern batteries in old NiCad chargers .
That's a very valid concern indeed. While some NiMH batteries will tolerate continued trickle charging (which is what many NiCd chargers will do), some won't and will have their lifetime cut drastically. Moreover, I have the impression that the original NiCD chargers doesn't charge the cells individually, which is a poor design choice to begin with. Better charge cells individually.
In general, it's best to charge batteries with the charger intended for that specific battery chemistry. Yes, it sounds kind of obvious...because it is.
I want to change Ni-Cad batteries (dead) to metall hybrid batteries.
I suspect the cells will be AA-sized. If so, in principle any NiMH AA cell will work as a replacement. Voltage is about the same and should present no problem.
Ideally you would make the cells easily removable so you can charge them in any generic NiMH charger (e.g. the kind that plugs directly into a wall socket). You could try to modify the existing battery pack by adding a removable flap/section to it or something. Or perhaps recreate the battery pack using 3D modeling & printing, but modify the design so the cells can easily be removed one by one. Since the battery pack sits inside the flash unit and is protected by it, some kind of open frame design would work.