Hello Everyone,
We're currently migrating our users to the new Chromium-based Edge and I wanted to provide some of our "lessons learned."
1) Upgrade Connector to at least 10.3 Update 3; this is when they added more official Chromium Edge support and you'll need this version for it to properly recognize the URL path in Edge.
2) Setting the necessary flags to allow Connector to communicate with the browser in the shortcuts works, but it only applies to the shortcuts you update and can cause some frustration with users.
For example, if the browser isn't open and it launches by default via an email link, the shortcut flags won't be applied and you could end up with users questioning why Connector isn't working.
3) If you need IE Mode, which unfortunately many of us do thanks to legacy sites and application, then the remote-debugging with JavaScript option will not work.
Remote debugging disables IE Mode; they are mutually exclusive. Instead you'll need to use force-renderer-accessibility and UI Automation if you want to have both options.
For Item 2, what we ended up doing to address the issue is to update the registry instead of updating individual shortcuts.
We located:
HKEY_CLASSES_ROOT\MSEdgeHTM\shell\open\command
and added the flag to the value of (Default):
"C:\Program Files (x86)\Microsoft\Edge\Application\msedge.exe" --force-renderer-accessibility -- "%1"
(You could do this with the --remote-debugging-port=9222 flag instead if you don't need IE Mode).
The goal was to force Edge to open with the flag enabled regardless of how it was launched (desktop, taskbar, start menu, email link, etc.).
There's a separate registry key to update under MSEdgePDF if you want to apply that when Edge is the default for PDF viewing, but who actually does that? 
If you can't, or don't want to, edit the registry, another option might be to create a sort of "helper" file. Basically, you rename msedge.exe and create a new msedge.exe file that just opens "msedge-original.exe" with the desired flags; this way anything referencing msedge.exe hits your custom file, which in turn runs Edge with the desired flags.
Chrome uses the same flags, so you could do the same thing if that is your default browser (the registry path is ChromeHTML instead of MSEdgeHTM)
If I missed something or you have a better solution, please let me know!