Just a minor correction, whitening does not make “the dimensions (channels) statistically independent of each other” – it merely decorrelates the channels.
Otherwise, your approach sounds reasonable and I agree with @richard to just compute all ICs, since your application is finding ocular ICs. These will always be among the first few ICs, so it doesn’t really matter if you compute all ICs or only e.g. 20.
I would not, however, reduce (compress) your data with PCA prior to ICA, but rather keep all PCA components, because this might negatively impact ICA decomposition (it might be necessary in specific situations though).