How did you come to the conculsion the Russian "х" is voiced? You are a native speaker, aren't youIt is a voiceless consonant. This is that sound: Voiceless velar fricative - Wikipedia, the free encyclopedia.
It can only become voiced when followed by a voiced consonant immediately (i.e. without a pause), any of "б, д, г, ж, з". Compare (sorry for the rude example, but it is only for the pronunciation sake): Он сдох (voiceless final "х"), but Он сдох бы (assimilative voicing takes place). Although Russians do not usually notice this voicing.
Moreover, the southern Russian "г" and the Ukrainian "г" are not the same! It's a mistake when some people think they are the same.
Souhern Russian "г" is exactly the voiced counterpart of "х": Voiced velar fricative - Wikipedia, the free encyclopedia.
The Ukrainian "г" is the voiced counterpart of English "h" in "hot": Voiced glottal fricative - Wikipedia, the free encyclopedia.
And the English "h" in "hot" itself: Voiceless glottal fricative - Wikipedia, the free encyclopedia.