Whether you use a shop safe, gift card, your own credit card, it doesn't really matter. Every credit card offers protection against unwanted purchases. As navybanker points out, even if you do cancel, you have to do so prior to the renewal date or they will prorate the charges daily at the high rate. If you truly cancel and you receive a bill for a few days, you better pay it. Who wants a ding on their credit for a few bucks?
Another nasty trick they pull is to send out the bill (If you choose to not have your credit card on file) on the day the service renews. So, by the time you get the bill, you're a few days into the new contract.