Last time when I do something like this, I used a long plastic cylinder and put it on the old sand bed. I then add the SD sand, unrised, thru the cylinder. Obvioulsy, the water within the cylinder was very milky, but because it is pretty isolated from the rest of the tank, it did not ruined (visually) the rest of the display tank.
Maybe a hassle, I guess...
If I have to do it again, I would just add some freshwater to the sand, and add the wet sand to the tank. If you care about the silt, just save the milky water and sell it like some companies
roll), or add it to the tank later.
In addition, there are some people who claims that bacteria on the silt will make the sand settle faster. If you are ambitious, you may want to run a mini experience and see if it is the case. Separate the milky water into two parts (use saltwater this time). Add some live sand from the old tank to one of them. Wait a few days, and shake both vigorously. See if the one with live sand will settle faster (I doubt it, but I never do the experiment...)