Even the smallest nuclear weapon, suitable for destroying just an enemy base, is still very likely to produce fallout that will spread to civilian populations.
Wrong. The smallest nuclear weapon (let's say, the W54 warhead for the Davy Crockett nuclear recoilless rifle) with a sub-kt yield will not cause any fallout if airbursted over the target at an altitude high enough for the fireball not to touch the ground. What you should be concerned about are high-yield nuclear devices detonated above the stratosphere: no fallout but the EMP will send your whole country - and with enough of them your whole continent - to pre-industrial levels in a flash. Say goodbye to your industry, your economy, a lot of people (who will die in accidents related to equipment not working anymore) and your once proud nation is ripe for the picking.