Should I use H2O2 on these Coins?

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I found an 1787 Connecticut Copper a couple of months ago. I can see enough details to determine that it is indeed a 1787 Conn. Copper. I would like more of the detail to show, including the date. As of now, I can make out the "17" and a bottom of an 8. Would using hydrogen peroxide on this coin help bring out the details that might be behind the corrosion, or should I keep it the way it is? Would it work on the 1809 Half Cent without destroying it? Thank you.

My coin is the one at the bottom of the photo. The one at the top is an example I found on the internet.



My 1809 Half Cent

 

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