The Wikipedia article quotes Solow from Inside Star Trek
saying that the soprano voice was dropped after the first season due to rights issues, but Solow was misremembering. In fact
, the first-season theme had two versions that were both instrumental, an electric violin version arranged by Courage and a cello version arranged by Steiner. The Courage-arranged soprano version was used in seasons 2 (conducted by Courage) and 3 (conducted by Wilbur Hatch). Probably the reason for the confusion is that the electric violin in the early season-1 arrangement sounds kind of like a soprano voice.
Now that I'm hearing The Cage score in such great quality and clarity, rather than the smear-a-thon we've lived with since the mid-80's, I can detect a soprano during the credits. I never heard that voice before, which is a real eye (or ear) opener.