The questions to ask yourself are -
What do you plan to gain by making the change?
How deep is the current sandbed?
How deep will the new sandbed be?
You may not have a lot to gain by changing the sandbed, but this depends upon what you are trying to do with the system. You also might want to consider a bare bottom.
Assumeing you still want to do this, you can change out a shallow crushed coral sandbed (under 1" deep) by the method you propose.
However, if you have a deep sand bed things get a lot more tricky, because now you have to deal with the anaerobic layer that will be under the top 1" or so of crushed coral. This can create a real mess if it gets into the water.
In the later case, my first choice would be to tear the tank down and set it up from scratch, but this is often not possible.
My next choice would be to do it this way -
Wash the major dirt, dust etc out of the new sand. You will not get it perfect, but get the worst out.
Prepare new SW so you can replace up to 75% of your existing water if necessary.
Remove and save a few handfulls of sand from the top 1" layer of the old sandbed.
Remove the LR for the time being. If you have room in the tank, you could shift all the LR to one side of the tank, do one side, then shift the LR to the other side of the tank and do that side.
Syphon out the old sand bed, removing as little water as possible. Do not add water removed back into the system.
Add the new sandbed, using the washed material.
Replace the LR.
Use the few handfulls of sand to seed the new sandbed.
Refill the tank with the new water you mixed.
This is quite a project. So make sure you really want and need to do it first.