The way I’ve always skinned mine when I do the filleting, all I do is leave a little skin attached at the tail when I remove the fillet from the bone side. Then I flip the fillet over and use the tail and the waste part to hold the skin while I run the knife down between the skin and fillet. The knife does have to be sharp and it is a pain if you cut to close to the tail and have to use you finger nail to hold the skin if it the skin breaks off.
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may your livewells stay full, and your rods stay bent.
Kevin