My four day old fry are fine. I don't appear to have lost anyone because of the move. As long as the water is from their tank and you aren't chasing them around for an age trying to catch them, I see no issue with moving them.
I have to move my fry at an early age if I don't want to risk them to be eaten by both/either parents as I don't have separate spawning tanks.
I would say it was more of a risk if they still had their yolk sacs attached or weren't free-swimming. Even so I have moved fry that young (dad is a fry eater) and only lost around half of the very small spawn.