I tend to cradle the rootball at the base of the stem with my fingers rather than dangling them by any of the leaves (longer roots can dangle). If placing in a narrow container that my hand/fingers won't fit, then I use a plastic spoon or fork.
-- taking out -- It's easy with individual cups and containers, just support the top of the soil mix with your fingers spread to gently hold the stem and/or with fingers supporting the soil between the seedlings, then turn the container over so the drop to the work surface (if accidentally spilled) is no more than an inch or so. Sometimes you need to gently tap the top edge of the (upside down) container against a solid surface (which needs to be tall enough so the plant isn't mashed into the work surface in the process).
...I still have frustrating time with cells unless the seedlings are overgrown and rootbound enough to push out from the bottom or thunk loose then pull out by the sturdy stems. I haven't got the hang of using knives or forks.