1942 Lincoln Wheat Penny Die Cracks?

I have never used the Verdi Care, but I have heard positive things about it. It does appear to help the appearance. I have always been one that doesn't like to clean a coin with anything but soap and water, and then only if it is pretty dirty. From what I have read, Verdi Care is to protect or preserve the coin more than a cleaner, but it does remove some of the verdigris.
I am guessing that a lamination like yours, cleaned up properly, should be worth $10.00 - $25.00.
Get some Verdi Care and some new 2X2 holders, it should be worth it!

Do NOT do this. You will regret it.

There are tons of posts here that will guide you to SAFETLY conserve your coins. Follow those.

Vinegar will remove the surface of the coin turning the coin pink in color. I would leave it alone for now. Experiment on circulation coins until you get a technique down first that works. Then think about it again before you might ruin a collectable coin. Removing the green removes part of the surface of the coin. So I would leave it alone.