How do I transfer an edited version of a photo in one LR catalog to a new LR catalog that has no edits.
I would suggest you to first export the Collection that has the edited images.
Then you can merge that Catalog to the other Catalog that you want.
Please check the article for how to merge the Catalog : Merging Individual Lightroom Catalogs into a “Master” Catalog « Julieanne Kost's Blog
Let me know if it helps.
Hint! The Lightroom Catalog is a database file and does not contain actual Photo Files, all it contains is info about the files you have imported and the info about the work you have done with the original image file.
Please provide info about what you are trying to achieve.
The normal workflow is to create one Catalog of the original files and then you can have Collections, Smart Collections, Virtual Copies to make alternate options.