If its overheating due to dried up paste yes it will make a big difference. If something else is causing your high temps like dust build up, or the cpu is under unnecessary load or both it likely won't do much.
Yes why wouldn't it be safe? Assuming you can take it apart and put it back together properly, the age of the laptop is not going to make it unsafe to change the paste. Do you need to change it? Is it overheating?
If its overheating due to dried up paste yes it will make a big difference. If something else is causing your high temps like dust build up, or the cpu is under unnecessary load or both it likely won't do much.