You need to know the details of modulation, not just frequency - it might be something simple like GFSK or OOK, but it might be frequency-hopping or spread-spectrum. Even if its a simple modulation scheme you need to know baud rate, encoding, and possibly have to deal with encryption or whitening.
The nRF24L01 module is limited to just two baud rates, BTW, so its unlikely to be useful. Its also obsolete, the nRF24L01+ has 3 baud rates (!)
Since the owner's manual gives no technical information beyond what size battery it takes it's very hard to say what frequency range is uses. Perhaps if you open the watch there will be a chip with an ID number you can look up.