There is no problem under normal circumstances, but problems may arise in extreme cases because chargers and power banks adjust the charging voltage according to the battery power, so the voltage is not very stable, especially when using electricity. When the load is large, they may increase the charging voltage, which will cause problems with the phone, such as excessive heat or damage.
The charging modules are all similar. As long as they match the capacity, are protected against overflow, and shut down when fully charged.
The key issue is one you need to pay attention to. if the battery used in the headlight is 3.7V, otherwise when the lithium battery is fully charged, it will be 4.2V (if fully charged is 3.7V, it will be 3.7). use it, you can use a boost moduleor step-down. Just be careful not to misconnect the positive and negative poles.