I have a small collection of e cig batteries similar to what you've pictured. I find these cells perfect for powering cheap led flashlights.
If you couple them with a TP4056 board, you need to change out the resistor that sets the charge current. While tricky, removing and soldering the surface mount resistor is doable by hand. I set the current to 250mA rather than the typical 1A.
Alternatively can add a protection circuit salvaged from a cell phone battery or other protected cell.