I was in a regional production of THE SOUND OF MUSIC many, many years ago and I played Kurt Von Trapp. According to the score we had for that production, Kurt sings the solo part of the children's portion. I sang it in that production. I have seen many productions where Kurt sings the solo part. However, I have also seen productions where it was sung by Leisl or Louisa as well. But I believe that in the score the part is given to Kurt. So the person who sings it on the Original Broadway cast recording is most likely the actor who played Kurt.