A little "9V radio" size of Ni-MH rechargeable battery produces 7.2V and has a capacity of 150mA/hrs. It has an internal resistance of 1 ohm and therefore will have a loaded voltage of 6.3V when charged. Its voltage will drop to 5.5V when it will need recharging.
If your 4W transmitter is 75% efficient, it will draw 5W from the battery. If the transmitter is designed to be operated with a 6V supply, the average current from the battery will be 833mA and it will last about 11 minutes.