If you want to store a pad, let it dry out on the counter and keep in on a shelf somewhere at room temperature. It will keep this way for a long time and only the cut part will dry out.
Catus pads will last for months if left out in the open. Keep it out of direct sun, but leave it sitting out, no bag, no box, somewhere with very good ventilation.
I did freeze cactus pad. It does turn into mush. However, I have also just done it with chopping it very small and then vacuum sealing it and it's not bad.
I always freeze mine, but I do wrapp them up pretty tight leaving as little "air" as possible in the freezerbag. When I want to give my two torts a little treat I cut of part of the frozen cactus and chop it up while it is still frozen. Then I let it defrost. Works fine for the torts and me.