I never remove my wedding ring Generally, I do not take anything valuable with me on vacation (other than my wedding ring, which is probably worth way more to me than anyone else, LOL).
I do not remove my athletic shoes but I am sure there is no metal parts on them. Sometimes the TSA agent insists - they usually don't at MSP and MCO). FWIW, my advice is to wear socks and easily removable shoes when traveling by air - I for one do not want to walk barefoot anywhere in an airport - who knows where all those other people's feet have been, YCK!

Anyway, something to consider regarding the toe rings.
FWIW, I put my watch, earrings and necklaces in a plastic bag and stuff it into my purse at home just before we leave. I put them on after I get through security. I do whatever I can to get through security as quickly as possible and try to minimize any chance of special security - I am paranoid that my things might get stolen while they are checking me. Usually send my DH through first with instructions to wait and catch my things if I'm not the very next person through, LOL. All he usually has is a wallet and shoes, LOL!.
Way more than you wanted to know, I'm sure. My advice is to not wear the toe ring or any valuable jewelry (except a wedding set) through security. If it gets you stopped for extra checking (even though you probably won't), it's just not worth the stress of worrying about your other things getting stolen.
Best wishes-