Is there an alternative way that won't bend my cards?
The best way to spring without damaging the cards is to be good at it, otherwise you might put too much pressure on the cards and overstress them. Even then, this move will bend the cards one way and break the cardboard fibers unevenly. Therefore, if you string the cards on both sides, you will even out the fiber-breaking (which leads to your cards being evenly broken-in). Finally, put your cards in a card clip so it can return as flat as possible when the internal stress is released. They won't be perfectly flat, but they will fan evenly everytime you'll get then out of the clip.