'Ringworm' is a common name for a dermatophyte or skin fungus... it is not a worm or even closely related to any kind of worm. Its much more closely related to athlete's foot fungus. Most fungi can be cleaned off of household items, but anything that is impossible to clean might be a candidate for disposal, as the fungal spores can last a long time in the enviroment

You can destroy fungus on almost anything with vinegar & water or maybe a very mild bleach & water solution;
be sure to rinse it like you're an obsessive compulsive clean freak.