It really depends on how deep your current sand bed is and how old it is. Using old sand has a HUGE risk of a nitrate explosion from all of the stuff deep in the sand bed. Personally, I think it's too risky.
It's a pain in the butt to rinse sand (I'm assuming you have 30-45 lbs of it. Imagine that in buckets full of water. Where are you going to do this? You dont' want sand in the sinks. You don't want to make a mess on the floor. If you really want to do it, you can rinse it with saltwater or even RO, but don't use tap water because of the chlorine.
Frankly, it's easier to just buy new sand, add about 10% of your old sand for bacteria if you like. But, if you are committed to cleaning it, as long as you rinse, rinse, rinse, you should be ok. Don't take too long during the move and be sure and test the water before you put your livestock in. If it's bad, I'd keep the fish in buckets with heaters and air pumps until you're SURE your new tank is ready.
Good luck!