Can battery be charged outside of case?

Single cells can be charged using a regulated power supply set to a voltage of 4.2 V, and a current limit appropriate to the size of the cell you'd want to charge, say about 0.5C - which means, if your cell has a capacity of 1000mAh you'd set the current limit at 500mA. A seasoned electronics engineer could slap together such a circuit from parts in the junk drawer. Carefully check that the voltage doesn't drift upwards as the circuit warms up under load, and adjust accordingly if it does.