The thing that makes a nuke "dirty" is completely unavoidable, as far as I know.
A nuke emits two deadly products: radiation, such as X-rays and gamma rays; and actual subatomic particles--free neutrons, alpha and beta particles, etc.
Radiation DOES NOT make matter radioactive! It's simply another form of heat. Infrared radiation coming from your stove is radiation from the red end of the spectrum; X-rays and gamma rays are exactly the same form of energy, except that they come from the blue end of the spectrum. Since X-rays and gamma rays have a higher frequency, they can penetrate your skin and burn you on the inside. That's what makes X-rays and gamma rays so dangerous.
Fallout, on the other hand, is produced when subatomic particles from the nuke are absorbed by the nucleus of a nearby atom, changing that atom's properties. A normal, friendly atom of non-radioactive carbon-12, if it absorbs a couple of neutrons, becomes radioactive carbon-14.
There might be some forms of nukes designed to emit lesser (or greater!) amounts of free subatomic particles, but in the end the one factor that makes a nuke "dirty" is if it's detonated close to the ground, exposing the ground to a larger amount of particles and producing more fallout. The fact that the blast wave pushes more of that fallout into the air doesn't make it any cleaner, either.
In the end, however, the basic idea of a nuke remains the same: to kill you.