Putin drops nukes the fallout hits Europe. It's WW3 no matter what if that happens.
I'm not sure nukes work like that anymore, but i could be wrong.
I don't believe any nuclear blast can be entirely without fallout. How much there is depends on the size and quality of the nuke and its upkeep. To avoid fallout you have to ensure that the radioactive material is used up as efficiently as possible in the initial blast. It also helps to explode it away from the ground i believe.