I understood that part.
If you use your existing sandbed you'll probably have a cycle. When it gets disturbed all the anaerobic bacteria colonies will die, and you'll free up any decaying detritus that's in it. If you have to use it I'd wash it as well as you can with the old tank water to try to remove the detritus, and as much of the dead bacteria as possible. But even doing that you're likely to have a small cycle.
If you go with new sand, new cured LR, and use 50/50 old water/new water you shouldn't really have a measureable cycle. Of course if you're using the old sandbed and wash it, you may not have enough of the old water to maintain this ratio. The 50/50, is so that you're not shocking your corals/fish with totally new water, in case some of your parameters don't really match up with the new saltwater, and because with some of the old water you'll get some of the bacteria culture that's maintaining your current tank, which will help jump start things in the new tank. Having fish in the new tank you'll run the risk of a cycle if the bacteria cultures aren't large enough to handle the ammonia output from the fish.
I'd make sure I had enough tests to do a couple a week for the next month, and I'd be prepared to do a 30% water change bi-weekly in case my tests started showing a cycle. Your corals and fish will be able to handle it if the tank cycles again as long as you're getting rid of the waste via more frequent water changes. It's a PITA, but hopefully you won't have enough of one to warrant it. I'd just try to be prepared in case.
B