Nurse scored a spectacular long-range strike at Crewe on Saturday as the Daggers won 2-1 but picked up an ankle injury late on and will sit out the trip to Wales.
That could see Josh Scott for make his debut after he completed a three-game suspension picked up last season with Hayes & Yeading while Wesley Thomas is also in contention to start.
Thomas had been a doubt to face Crewe thanks to a knock but he came on as a substitute at Gresty Road and could feature.
Mark Nwokeji remains two weeks away from a return to training as he continues his eight-month lay-off with a cruciate knee ligament injury.
Defender Anwar Uddin has not trained since the first training session in July due to a bang on his leg and is still out.