Is it possible to move live rock and live sand from one tank to another with out causing a cycle if it's done carefully and doesn't come in contact with air?
Most advise against moving sand from one tank to another. There a lot of stuff in the sand and if you stir it up is can cause a cycle in your new tank. I've heard of it being done, but when I up graded I decided to just new sand and added a few cups of the old sand to feed the new sand bed.
If your sand isn't old, it's fine. I would rinse it with you water from the tank. If you have pistol shrimp your more than fine as I find them to be the best in flipping your sand over (you'll never have a system crash with those guys in there), but they love to mess your sand bed a lot and steal frags!!