Question about normalization before estimate the spectrum
Most standard time-frequency-scale transforms are consistent with mean/standard-deviation corrections. In a more pedantic ways, linear transforms can cope well with affine transformations, in the shape of:

$$x' =  \frac{x-a}{b}$$

of which the $z$-score is a special case. The potential bias can easily be inverted. 

So as long as the representation remains linear, and somehow preserves energy, such a normalization does not sound so harmful to me. With CWT tools, you can compare shapes. However, you loose amplitude, stuff becomes relative