Well how well do you know the cards? Sometimes tools develop a sort of personality all their own and that can affect what you choose to do to cleanse them. So you might want to take a moment to clear your mind, hold the cards, and just ask how to cleanse them. The energy of the cards itself may have a suggestion for you.
Failing that, here are some extremely simple sage-free ways to cleanse cards.
* Banishing Ritual - sort of involved and Hermetic, but takes not tools!
* Sunlight and/or Moonlight - don't just leave them sitting outside, but deliberately offer them up into the light of the sun and moon to be purified by the Mother and Father
* Oil - you obviously need to be careful when deciding this since oil could potentially damage the cards. I've had great success though with touching the sides of the deck with oil (so I touch the four edges of every card), though you should certainly stick to lighter oils, not heavy thick ones.
* Other incense, smoke, or wind - Divination, particularly tarot, is an Airy art. It would therefore be totally appropriate to cleanse them in an Air-specific way. You could even generate wind by wafting the cards with a feather or centering, grounding, and cleansing yourself and blowing on them.
* Holy Water - you would likely want to touch the edges of the deck as I did with the oil, but this should work great too.