Just nit-picking, but fallout does not blow around in the "long run", it falls and then stays. So they can just pick a day when then wind blows the other way.
That is not to say fallout wouldn't wreak havoc elsewhere, though. Thinking you can have "bunker busters" that dig in deep enough to limit fallout is a mad fantasy. If anything, a partially-buried nuclear explosion will worsen the fallout significantly by irradiating the soil around it and then throwing it up into the air.
Here's something about bunker busters:
http://www.ucsusa.org/global_security/nuclear_weapons/nuclear-bunker-buster-rnep-animation.html