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.