Yeah, it will be based on the user used to scan the asset. Browser settings are user specific after all so I don't know if there is a workaround for that.
The only way I can see to do this would include some more custom database work. Basically, you could scan the registry key that you mentioned to scan the user ID. Once scanned, you can use an SQL script to create new custom registry scanning targets.
For example: HKEY_USERS\S-1-5-21-4219328981-2174278074-3449214681-1001\Software\Microsoft\Windows\Shell\Associations\UrlAssociations\https\UserChoice\ProgId
That way you could always scan the last user's default browser even if you are using an admin account to scan. You would obviously have to change the report I linked a bit to compensate.