The voicing thing is known as rendaku. Generally it's a bit of a mystery when it will and will not happen. This thesis lists a bunch of proposed rules, two of which seem relevant:

• Rendaku is favoured if the compound words are native-Japanese (yamatokotoba). This might be the reason for kozukai vs mahoutsukai, ko is native-Japanese and mahou is sino-Japanese. So by analogy, one would not expect voicing for beizutsukai.

• Noun+Verb compounds exhibit rendaku if the noun is an "adverbial modifier" but none if it's a direct object. In "using magic" 魔法を使う magic is a direct object, so no voicing. On the other hand kozukai ('little servant'?) is an Adjective+Verb, which explains the voicing.

In any case, I guess the upshot is that we should expect beizutsukai, without rendaku,