I think you should be okay to run both EDFs using one battery and the 4500 mAh 4S you specified should give you reasonable run time provided you are not at 100% throttle (40Amps each motor) for the whole flight.
One thing to confirm is which 50mm EDF you are getting? I see that there are two motor options available, a 4500kV (suitable for 4S, 850g thrust at 40Amps) and a 5400kV (suitable for 3S, 650g thrust at 40Amps).
DamoRC