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Dremel, RotoZip, small router...even a razor knife or sharpened can opener or other "sharp" scoring the same lines several times until you cut through. In this case the Dremel might work better because even if it is not as powerful, it may be easier to use a flex shaft to get into tighter spots with it.
As often as not, once you remove the skin you'll find the core material is in need of replacement as well.