But what will a coin cell do when it's trying to get charged? That sounds a bit worrying.
But I didn't realise that. Perhaps I could use a voltage divider then or simply input 5V. 5V is too high for a battery but most devices accept it there anyway.
> But what will a coin cell do when it's trying to get charged?
You can get rechargeable lithium coin cells. It will just recharge fast.
The cell usually has enough internal resistance and surface area that it can't overheat or violate the charge current limits.
I still wouldn't recommend this approach, simply because the DC/DC converter approach you specified is slightly more power efficient (onboard chargers tend to have poor energy efficiency - many are simple linear regulators from 5v!).
But I didn't realise that. Perhaps I could use a voltage divider then or simply input 5V. 5V is too high for a battery but most devices accept it there anyway.