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glahana 

There is a way... Edge uses some of the same config as chrome.  So you can edit the master_preferences file located in: C:\Program Files (x86)\Microsoft\Edge\Application.

Add: "do_not_create_desktop_shortcut":true  to the distribution portion of the json, below is my edit from our installation.  Now this won't prevent the shortcut during installation since the install appears to use the file for installation in the msi. 

Since there is installation info in the file, I scripted editing the existing file rather that having a true "master preference" file just copied to the dir like chrome uses which only handles config not installation methods.

Whats even worse about this behavior... If you don't do the above... If you just delete the shortcut in the public profile... Edge will create shortcuts in each user profile at launch/update.

{"distribution":{"do_not_create_desktop_shortcut":true,"msi":true,"system_level":true,"verbose_logging":true,"msi_product_id":"2D0AE8FB-D52E-3D51-845F-FF1A7FFBB09E","allow_downgrade":false}}