Step 4Test!
Take the small piece of vinyl you saved, remove the backing to expose the sticky surface and stick it somewhere discrete on your laptop. Leave it there for some time (I left mine in place for a month). When you feel an appropriate time has passed, remove the vinyl and check that it hasn't caused permanent damage to the laptop casing.
If the laptop is old and you don't care about it you can skip this.
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but hey.. if my first suggestions didn't work i don't know what else would.
...also, there's a way to remove stickers that results in very minimal specs, if any, of glue. however, this process is 'prolly not good for an electric device. what is this wonder i speak of? i speak of soaking your stickered item in SUPER HOT water and slowly peeling the sticker off. or using a hair dryer while slowly peeling off. aside from these to methods burning you, they also, you know.. might KILL your laptop. so i would only do those if you REALLY DGAF about your laptop ;)
Here is a link to the ebay seller's listing: http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&item=180306580466&ssPageName=ADME:B:EOIBSA:UK:31.
Obviously I can't guarantee the vinyl stickers he's selling won't damage your laptop, as your machine is probably not made from the same material as mine. However, the vinyl I got from him was high quality and did all I wished it to. The other comments given here have sound advice for removing any residue that may be left if and when you choose to remove the skin.
Good luck!