How do I exchange LCD display with 7-segment LED's?
This may be more trouble than it's worth. The driver will probably put a ~30 Hz square wave on the backplane, and switch segments on by driving them with the inverse of that, and maybe even the in-phase signal when the segment is off. 



In that case the segment will always get a signal and then Oli's solution doesn't work. 

Even worse would be a multi-level drive; then the signal would look like this:  



Not pretty. It may be easier to just use the receiver and replace the controller with your own. The WWVB/DCF77 receiver will be a separate IC, and most likely connected to the controller via three wires: ground, data (from receiver to microcontroller) and enable (from microcontroller to receiver). The enable is required because the receiver consumes a few mA, and would drain the battery too quickly if permanently on. On one radio controlled clock, powered by a single AA battery I measured 3 mA with the receiver on, and 7 &micro;A with the receiver off.

The TI MSP430 family is known for its low power consumption. You'll have to write your own software, but the coding of both WWVB and DCF77 is kept very easy: the first decoders used common TTL logic rather than microcontrollers, which weren't available at the time. Microcontrollers can decode complex protocols, but with TTL you would need too many ICs, hence the simple coding and modulation format.