Eu encontrei a resposta aqui, e é um pouco louco: link
Além disso, não se preocupe com o registro - tentei usar outra resposta , e não chegou a lugar nenhum. A resposta abaixo funciona perfeitamente.
A parte relevante é:
First, make sure custom handlers are allowed at vivaldi://settings/handlers. [should be chrome://settings/handlers]
Then, close Vivaldi.
Use JSONEdit, to edit "C:\Users\yourusername\AppData\Local\Vivaldi\User Data\Default\Preferences".
Copy the following to the clipboard:
{ "enabled" : true, "ignored_protocol_handlers" : [], "registered_protocol_handlers" : [ { "default" : true, "protocol" : "mailto", "url" : "https://inbox.google.com/?mailto=%s" } ] }
Right-click on the root node in the Preferences file in JSONEdit and choose "Paste as child from clipboard". Then, rename the pasted object to "custom_handlers" and save your changes. (This is assuming you don't already have some custom handlers. If you do have some, you just need to add to the registered_protocol_handlers array.
In Vivaldi, go to vivaldi://settings/handlers [should be chrome://settings/handlers], click the 3 dots to the right of the inbox.google.com entry (that's now there) and choose "set as default". Then you can go into Default Apps in Windows and set Vivaldi as the default mail client. Then you should be good to go.
On a side, for Gmail (mail.google.com), it's:
navigator.registerProtocolHandler("mailto", "https://mail.google.com/mail/?extsrc=mailto&url=%s", "mail.google.com");