Are you offering cat chowder? Skinning a cat...eww...not much meat there. Would I skin you? No, too messy. Would I hire somebody to skin you when hunger strikes and there's nothing else to eat? Probably Yumm...runvardh on a stick...
ahhh, this problem was brought to my attention not so long ago, only for humans rather than cats. If you were in a war and someone ordered you to skin a man alive and take his bones, how would you get around playing with their privates? If you just want the bones though, you might be able to just cut up the top bits and then just rip the skeleton out of the rest of it. But skinning a cat would be kind of easy right? you could get a knife and just hack away and pull at all the messy bits, you could put it in a tub of concentrated acid and it would decompose the skin, but technically that's not really skinning the cat. If you attached some kind of clips to critical points on the kitties skin and suddenly pull from all angles you might acquire the desired result, but that method is a little tedious. You might be able to peel the skin off bit by bit with your fingernails or something. How about fire? You'd have to put up with the smell of burnt hair and maybe cat skin, but the method might work quite well if you do it outside.
I skinned a cat once. I was dissecting it for biology. Anyway, just a few well placed cuts with a razor blade and it's pretty easy from there. You have to hack away a little bit around the back, but really it was an easy job. I really would want to do it faster though, 25 minutes just took too long. Is the goal to keep the cat intact and skin it or you know...get the skin off. If so...I propose wrap it in firecrackers and shoot a few roman candles at it. Instant skin be gone.
Skinning... well if you want to recover an intact pelt, you should start at the belly... bisect at midline thorax to groin. Pinch skin around throat to make the first cut, then go straight down. Probably need a little bit of work at junction of the thoracic cavity and diaphragm and belly button. Then you blunt dissect to peel the skin away from the chest and abdomen. Once you get to the sides, stop and work at arms. Armpit first, incision along inside of arm to wrist... Now the skinning gets annoying with connective tissue around joints. Perhaps it's best not to keep the skin from the arms and legs... Anyways, same process for the legs. Start at the inguinal area and cut along inside of leg, be careful not to nick the femoral artery or vein or you get a huge mess and ruin the pelt. Skinning should be done freshly killed... stiff body makes it difficult but you do have to be careful of the blood. Anyways, after you get that done, flip it over. Again, start torso region first. Work upwards to shoulder. Shoulder is likely annoying. Hip should be easier but likely require cutting with scissors rather than plain blunt dissection. Finish around coccyx and you should be done. Not sure what you want with a kitty head... It's near impossible to skin.
edit: I'm merely informing... Afterall, I don't exactly want to skin this kitty.