It does happen: if the silvery surface of a piece of a CD came off, this does not mean the end of its usefulness.
one looks nearly in the same direction as the light source
since the spectrum is seen at an angle of about 20 degree from the light source, one can place at that direction behind the CD a dial which indicates the wavelengths.
although the spectra are less bright than with a CD in reflection. The construction of such an instrument is a bit involved. Here I can give only guidelines that allow you to design your own version.
Make Your Own Simple Spectroscope Would you like to see the colour in white light? It is quite easy to create a simple spectroscope using inexpensive items that can be found around your house.