You didn't say why you needed to wipe a magnetic stripe without otherwise damaging the credit card. Wiping it to prevent someone from using it to buy gas requires a different level of effort than wiping it to erase forensic evidence (and your question is tagged [forensics].)
Rubbing a neodymium magnet in small circles working across the length of the stripe will likely prevent the card from working in a gas pump, but it may not be enough to prevent a forensic examiner from determining the contents. Just because one specific mag stripe reader can't read the data doesn't mean that a remnant of the data doesn't exist that can still be picked up by a lab quality analysis tool. If you really have to be sure, there is a magnetic testing ink product out there that will display the lines of magnetism visibly, in black and white. You could use that to confirm your wiping technique.
Also, you probably should be aware that different cards use different magnetic technologies to record their data. Cards can be either HiCo or LoCo:
HiCo stands for High Coercivity. HiCo cards usually have a black stripe, and require a powerful magnetic field to change them. HiCo stripes are usually used for durable cards. Most, but not all, credit cards are HiCo cards.
LoCo stands for Low Coercivity. LoCo stripes are generally brown, like audio recording tape, and require a much smaller field to change. LoCo cards are often used on temporary disposable cards, such as in parking ramp ticket dispensers and hotel room keys.
Being able to wipe a LoCo card with a magnet doesn't mean the same technique will work on a HiCo card. In other words, practicing on a hotel door key card won't prove that you can successfully wipe a credit card in a hurry. Finally, using a magnet will likely leave forensically visible evidence that you used a magnet to deliberately erase the stripe, which may raise a different level of suspicions.