So a ream of paper is 500 sheets. You'll be able to search better by looking for the weight of the paper per ream, rather than the thickness.
https://thomasgroupprinting.com/how-is-paper-weight-measured/
Copier paper is likely to be a bit thinner than letter paper.
Careful about going too thin, or your printer will just shred it and jam up. Tissue paper for example is unlikely to work. Newsprint paper might be okay, but you'll need to look at the numbers.