I am looking for rubber bands that are not too elastic.
I remember with LEGO there were rubber bands used as a belt between rotating pieces:
They weren't the usual rubber bands that you can stretch much more:
Do you know what is their name?
O-rings are typically made from a firmer rubber than a rubber band. They will stretch but not as much. They come in all sizes, so you're going to have a shopping quest ahead of you, but "O-ring" is probably the best search term for you.