Find a protection PCB online (eBay, Deal Extreme, Aliexpress, battery websites e.g., orbtronic/all battery) for the protection side of things. Make sure the cut-off current is above the max current you expect to draw. Since you're replacing the batteries with lower internal resistance and higher voltage lithium ones, you'll want at least double the normal current. At a guess, 2.5A+.
When the battery is functioning normally (i.e., not over 4.2V, not under 2.5V, not drawing more than protection pcb rated current), the protection PCB is effectively invisible. You can connect a charger board to the protected battery without problems. A very common charger board uses the TP4056 which runs off of a 5V source such as a USB port.