Since you don't need them, why do you want to wear Reading glasses? It is unnecessary for you. If you have problems in close work, you are possibly suffering presbyopia. It is better for you to have an eye exam and have reading glasses made to your prescription.
You may go to an optician to have an eye exam and the optician will advise you what to do.In my opinion,you can try them on,if you can see more clearly with them on, it won't damage your eyesight;if you find no difference whether you wear them or not, it's unnecessary for you to wear them.
It won't damage your eyesight, but you may get blurry vision with them on if you don't need them. I would suggest you go to see an eye doctor and have your eyes checked. You can ask the doctor to recommend some reading glasses for you that suit you fine.
Oh, I think if you mean that you want to have a try, I think this will not damage your eyesight. If this pair of reading glasses can help with your vision problem, you may wear them in future. But I suggest you not to wear them in future. you may need to have your eyesight checked by an eye doctor first before wearing the reading glasses. If you really need a pair of reading glasses, you can buy a new one in an optical shop instead of using other's glasses.
I think reading glasses can damage your eyesight if you don't need them. It is said that it will damage our eyesight if we wear enhancing glasses for extended periods of time when we don't need them. We may get blurred vision and headaches usually for a few days. But if we wear them all the time, we may get permanent damages. of course our eyesight will drop dramatically. I think you'd better not wear them.