I think the correct version is without any apostrophe. "Peddars" is attributive (selecting a particular lane) rather than possessive (indicating that it is owned by or a body part of somebody). However, if you consider "used by" to be grounds for the possessive (as in "the dog's bowl", if you have one dog, or "the dogs' kennel", if you have two) then perhaps it should be Peddars' Way, as there would be more than one peddar, whatever they were.
Yours pedantically