I suspect that crest factor fingerprinting will confuse too many distinct waveforms. However, if you want to pursue this, its not difficult to generate your own table of crest factors using any programming language you can generate the waveforms in and implement peak detection and RMS calculation algorithms. If you are familiar with Matlab or GNU Octave, I'd start there, though my personal preferences for manipulating and creating engineering data tables tend towards writing console apps in 'C' or scripting Excel.
In theory, yes it can be done, as its possible to characterise a signal by spectrum analysis, comparing the relative power and phase of the fundamental and its harmonics, (which for a fixed frequency periodic signal is sufficient information to reconstruct the original signal subject to a bandwidth limitation of the highest harmonic used) and pure analog swept spectrum analysers can be built, as can analog circuits to sample the various harmonics phase and quadrature components and window compare their levels, but its impractical to do it that way, (and has been impractical for over 30 years) due to the physical complexity (I estimate a 19" rack mount cabinet full of eurocard size PCBs) vs sampling the fundamental and harmonic levels with a MCU (which became viable approx. 40 years ago), or even sampling the signal and using DSP techniques which has been viable for over 25 years.