Got a kind of helpful reply from a friend with a more technical background. He said that the specifications of battery matter, which would be stored on the chip, and if we get a battery which meets general specifications, there should be no problem, because the charge controller is part of the phone and would take care of the rest.
Just for the record, he teased me a bit because there are many offers for iPhone replacement batteries on ebay, but not a single one for a Fairphone. (sigh…)
I guess we should add to the FP2 wish-list that the battery will be the same as in the next upmarket best-selling Android phone. And probably, (not only) @paulakreuzer needs to start searching for additional sources for replacement batteries, just in case the Fairphone stock runs out. Reminds me, I should probably get a second one now, just to be on the safe side.
FTR, and probably for the benefit of people like @Hart travelling Asia: if my quick web search is correct, my best guess is the WS20S battery for the HonPhone V9 should be identical to the Fairphone battery. It’s available via some online sources, but it’s not so easy to get one in Europe. I could probably ask some colleagues in Asia to bring one (they seem readily available in Singapore), but at the current exchange rate, it’s even cheaper to buy one from FP.