Its OK to add the new sand with fish in there, it wont hurt anything, but if you dont want sand all over everything just get a cup and pour it where you want it and fan it off your decorations and stuff when you are done.
Think about this a second... if you wet the sand and add it to water, wont it just go all over the place? Of course. Adding it dry wont make any differance, as once it hits water it will do the same thing as wet sand.
DONT take your old sand out with fish in it. It stirrs up all the crud thats accumulated. I know a few people in the SW
fourm stirred it up too much and killed all their fish.
Can you save as much of your tank water as possible, and just store it and the fish somewhere else until its done?
Also I would save some of the old gravel to keep some of the bio media in there (If you just keep a little bit and mix it with the new, you wont see much of it at all).