I think a good exercise to do before you do data augmentation is asking yourself, whether you would be able to identify what you want to predict from your data. Also, it is worth just trying to look at your ideas and see if these result in better validation accuracy.
Using Gaussian noise is potentially a good idea. The level of noise that you want to add, depends on your empirical estimate of the signal to noise ratio, which is possible to calculate. If you think that the noise varies through the wavelenghts, you could try estimating the signal to noise ratio for each wavelength bin to confirm. Also these spectroscopy devices often have a datasheet which contain information about their noise behaviour calculated respect to some reference.
GAN or some generative ground truth model
GANs could be also exploited here to do data augmentation, then the generative model could be validated by a human observer (but this really depends on what you want to predict). Other kinds of ground truth models could be also constructed like adding Gaussians at relevant wavelengths and noising them.
You could also try small shifts in the spectra so that your algorithm is robust to some uncertainy in the wavelength calibrations.