Since April 28th, Cortana restrics Microsoft Edge as it's browser to force Bing upon users.
SearchWithMyBrowser is a little utility that associates itself with the microsoft-edge: protocol, used by Cortana to open Edge. It will then simply redirect the request to your default browser.
To use another search engine than Bing, please refer to this documentation.
This program is licensed under the WTFPL.
A little batch file, make.cmd, contains everything you need. Simply run it.
If you want compile it manually, simply call csc.exe, from Roslyn version 1.2.1 on the file SesrchWithMyBrowser.cs with the target winexe.
Once again, install.cmd should fill all your needs.
If not, simply move the file SearchWithMyBrowser.exe to a permanent location (the file will need to remain here until you uninstall SearchWithMyBrowser) and call it as admin with the command line option /register.
If you're even more paranoid, manually create the registry entries, either with a .reg file or the Registry Editor:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\SearchWithMyBrowser]
"URL Protocol"=""
@="URL:SearchWithMyBrowser Protocol"
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\SearchWithMyBrowser\shell\open\command]
@="\"C:\\Something\\SearchWithMyBrowser.exe\" \"%1\""
[HKEY_LOCAL_MACHINE\SOFTWARE\SearchWithMyBrowser\Capabilities\URLAssociations]
"microsoft-edge"="SearchWithMyBrowser"
[HKEY_LOCAL_MACHINE\SOFTWARE\RegisteredApplications]
"SearchWithMyBrowser"="Software\\SearchWithMyBrowser\\Capabilities"
If you appear to not have used the provided install.cmd to install the program, you can run rundll32.exe shell32.dll,OpenAs_RunDLL microsoft-edge: to then set SearchWithMyBrowser as the protocol handler.
Simply call it as admin with the command line option /unregister, and delete the file.
Or manually reverse the registry change you made while installing it and delete the file.