There's a good explanation of the registry settings for the default mail client in this thread:
Where Windows 10 stores default email app in its registry - Super User[
^]
Essentially, you need to start with the
SOFTWARE\Classes\mailto
key under HKCU/HKLM, but there are other keys which can override this:
SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FileExts\mailto
SOFTWARE\Microsoft\Windows\Roaming\OpenWith\UrlAssociations\mailto
SOFTWARE\Microsoft\Windows\Shell\Associations\UrlAssociations\mailto