Even with the worst of lag, the precision will be much better than that lag (about 10 ms to where you are). I would be worried about multi-paths and such affecting precision, but their contribution to what you are doing would be trivial. As for accuracy, I doubt your wristwatch holds 10-ms absolute throughout the day, which begs the point, how did you synchronize it that closely? You have a bionic finger too?
BTW, as mentioned in another thread, I get WWVB well late at night, but in the afternoon, my reception is sporadic.
John