Can those stainless steel lug nut covers be removed without ruining them? I am needing to rotate my tires, but I hate to distort these covers if I can avoid it. Thank you

no just chisel them off and get a new set they are cheap on ebay-i had the same problem-best thing i ever did was get rid of those caps

Can't you just use the correct sized socket? Or are they damaged already?

Norri, they are not damaged at all; I just wanted to prevent any damage. I have a lug wrench the correct size.
I believe I could possibly use tape on the inside of the socket area and prevent any scratches. I have also seen sockets and wrenches with protective sleeves on the contact areas.
Maybe I am too protective of them.