You won't really be able to dye them- it sounds from your description that the shoes were created through a molding process and the yellow you see is the colour of the plastic itself. Your best bet would be to basically "paint" overtop of your shoes- but you will need to find a paint that will both bond to plastic and be flexible enough to withstand the wear and tear of walking.
Although i don't know the solution to your problem, i hope this helps ya on your way to finding one.
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"Asking a bomb squad if an old bomb is still "real" is not the best thing to do if you want to save it." - denim
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