Yes those electric dog nail grinders are safe for dogs and cats to grind their nails down.
I've never used them myself but my friend has one and uses it on his dog and it works great although the dog gets a little bit scared at first but after a few seconds the dog calms down and the dog is now getting used to the electric dog nail grinder and he's not as scare of it as he used to be.
The electric dog nail grinder works great on my friends dogs nails and I would certainly buy one if I needed one but as of now I just use the nail clippers for the dogs nails.
But I may buy one of those electric dog nail grinders eventually.