The problem you've got is that even if you could time shift the signal, how are you hoping to compare it? You'd need to compare a distinct time-slice of both signals, not the instantaneous value of both signals because otherwise you could easily get a false trigger that the waveforms are the same when infact they are not.
To my mind, the only way to compare a "time slice" of two signals is to digitise them both and do some maths on them. ie a microcontroller or a DSP, which you have already specified as not being allowed.
I think my earlier suggestion would be a better route to investigate, but it seems I was right to question whether my idea would work for complex waveforms. You'll need to research into breaking a signal down to it's fundamental - have a look at comb filters as RonH has suggested.
Brian