Removing the card is simple. Covering them with a material like suede would take a bit of care, but it could be done.
You would need to pad it from behind to give it 'body' or else it will just look flat. Go to a sewing shop - the padding or filling they sell for lining patchwork quilts would do the job.
The covering material would need to be stretched tight over the padding. Depending on the model there ought to be enough door 'furniture' to compress the covering/padding in at various points to avoid too flat an appearance.