According to this article CCI and Fiocchi, are the only ones making lead-free primers. It didn't say which sizes were or were not lead free, so I guess the next step would be to contact them directly.
Since some are critical of the age of articles that get posted, you will be relieved to know that this was published on March 19,2023.
If you have any questions about primer compounds after reading this, your chemistry knowledge far surpasses mine.
https://www.bevfitchett.us/chemical-analysis-of-firearms/priming-compositions.html
No info if any of the primer compounds affect Gun Skins.