I found the following as the simplest solution. Warning: Do not do this if you are not a local administrator.
Modify the following registry keys:
ProgId to be a nonsensical value.
Remove your local admin account from permissions on the UserChoice folder. (You will still retain admin privileges as long as you are in the administrator's group)
When clicking on a http/https link, Windows will look at that registry key to see what program to run. When it can't finds it, it brings up a list of all registered http handlers for you to choose from. Normally it would set whatever one you choose to that registry key, but it fails due to the permission being removed. It would work if it had elevated permissions, but that web browser selection screen does not have elevated permissions.
A hack, but it's working for me, and I believe it is safe.