Well, the answer that I really needed has been answered: Yes, you can transfer songs from a handheld cassette player to your iTunes library. I just did it, and the results were everything I had hoped for. (1) the quality was as good as I have gotten from desktop cassette players (2) The only piece of extra equiment needed is an iMic, which I already had.
The only reason that I had been having difficulties was that I was using the wrong settings. Everything was quickly clearly up when I talked to a technician at Griffin, the manufacture of the iMic.