Does the hand become impure if perfume is transferred to it from another hand, with dryness and only the scent remaining, and without knowing if the perfume contains alcohol?

Your action of abandoning shaking hands with Muslims for this reason is a mistake and a whisper (waswasa). The original principle regarding things is purity. The persistence of a smell on the hand has no effect, even if it is the smell of alcohol. Scholars themselves differ regarding the impurity of alcohol to begin with. Moreover, the alcohol substance added to perfumes may transform into another substance before its addition.