Final answer:
The safest cooling method is spraying the victim with water and then fanning them, as it uses evaporative cooling and avoids the risks associated with other methods that can lead to hypothermia or tissue damage.
Step-by-step explanation:
The safest cooling method for someone who needs to be cooled quickly, such as an individual suffering from heatstroke, would likely be spraying the victim with water and then fanning them. This method utilizes evaporative cooling, which is efficient in dissipating heat without causing too much of a rapid temperature change that might lead to shock or other issues. It avoids potential risks associated with excessively rapid cooling methods like ice baths, which can lead to hypothermia if not carefully monitored.
Cool water baths can also be safe if managed properly. However, direct application of ice bags should be used with caution to prevent local tissue damage from freezing. The priority in such situations is to cool the individual effectively but safely, avoiding any methods that may induce too drastic a temperature change.