Script Copy Dropbox Link to Apple Mail

It sounds like you're referring to the feature of the official Dropbox desktop client where you can right click on a file or folder and choose "Copy Dropbox Link" to get a shared link for that file or folder.

The Dropbox API doesn't offer a way to interact with the Dropbox desktop client itself, but you can use the Dropbox API to communicate with the Dropbox servers to get the same kind of shared link.

To create a shared link like that, you would call /2/sharing/create_shared_link_with_settings: 

https://www.dropbox.com/developers/documentation/http/documentation#sharing-create_shared_link_with_settings

Or, to retrieve an existing shared link, you would call /2/sharing/list_shared_links:

https://www.dropbox.com/developers/documentation/http/documentation#sharing-list_shared_links

Those are links to the documentation for the HTTPS endpoints themselves, but we recommend using one of the official SDKs if possible:

https://www.dropbox.com/developers/documentation

Those have corresponding native methods for the HTTPS endpoints. 

I can't offer guidance with the non-Dropbox side of things though, such as choosing a good programming language for your platform, or interacting with Apple Mail.