Setting default file associations is a complex process, normally involving an XML file to list the defaults and then using DISM to deploy the list. Read about it here: Set Microsoft Edge as the default browser
Here's a cheeky way of doing it that relies on Windows objecting to a change in the user's choice of browser. If you remove the user choice key from the registry, Windows should enforce its own default, which is Edge. The user should see a notification to this effect:
... at which point the user can of course change it to something else using the Default apps settings page.
You could create a simple batch file to delete the most obvious keys using REG DELETE:
HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FileExts.htm\UserChoice
HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FileExts.html\UserChoice
HKCU\SOFTWARE\Microsoft\Windows\Shell\Associations\UrlAssociations\http\UserChoice
HKCU\SOFTWARE\Microsoft\Windows\Shell\Associations\UrlAssociations\https\UserChoice
Please try this on a test machine having backed up the keys before deleting them, and come back here to tell us how you got on. You use my suggestion at your own risk!