Seems like it's about as good as anything else: http://forvo.com/word/%D0%BC%D1%83%D0%B6%D1%81%D0%BA%D0%BE%D0%B9_%D1%80%D0%BE%D0%B4/#ru
As I understand it, letters in Russian consonant clusters adopt the voicing/voicelessness of the last consonant in the cluster. к is unvoiced (it's voiced counterpart is г). Hence, ж is devoiced, and is pronounced like ш, its unvoiced counterpart. Word final voiced consonants also tend to be devoiced; hence род sounds like рот.
You see, devoicing the last consonant it not exactly a rule that defines the meaning of the word. It's just the way we speak. The same goes to turning unstressed vowels into a schwa sound.
It's entirely possible to keep the voiced consonants and enunciated vowels. People would understand you. The words would still mean the same. But you would sound funny and foreign.
However, when we, Russians, speak slowly and carefully, we sometimes do that too. That what the lady from wiktionary did. She overenunciated the word because she wanted to sound clear. Unfortunately it had a side effect of not sounding the way it would sound in real speech and confusing non native speakers.
The audio for the Belarusian entry is closer to how we say this word in regular speech.
Well мужско́й /mʊʂˈskoj/ has an unstressed first syllable, so that vowel is weakened to /ʊ/, the vowel in "put" or "should".
Make sure you're familiar with vowel reduction, it's at least as important in Russian as it is in English: https://en.wikipedia.org/wiki/Vowel_reduction_in_Russian