Detonating a nuke high enough to get widespread EMP damage is probably going to mean little or no fallout, especially with the kinds of devices that were used by both side later in the the Cold War (i.e. very efficient compact designs intended to allow as many RVs in a MIRV warhead as possible).
To really get a decent EMP, you need to detonate the weapon at an altitude of several hundred kilometers. Any fallout will just be added to the already massive amount of fission products in the atmosphere from previous detonations.
