I would not put any type of correction fluid (WiteOut, LiquidOut) on a puppy. These types of fluids are very toxic in odor and most schools have banned students from having them in their possession. (The sticky tape version is allowed.) Students were found getting high from sniffing the bottles and have even resorted to painting their finger nails with the fluid and sniffing their nails during the course of the day.
Scary stuff in my book. There are safer ways to mark your puppies - purchase a hair clipper and shave various parts of the puppy's body to ID them.
The tiny amount of volotile compounds in one brush mark evaporate right away and all that's left is a non toxic mark. The marks are nowhere near their noses. (Picturing puppies sniffing it out of paper bags)