I know this is a super-old thread, but for me it was the number one result on Google when searching "white edge icon", so I thought maybe I could help somebody.

I didn't want to change them manually, so I did it with some PowerShell. It may be necessary to change the permissions/ owner of the "Assets" directory or launch PowerShell as Administrator, or both.. I'm not sure as I tried a few other things in PowerShell and thought they weren't working as a lack of permissions, so I'm not sure what one has to do when they have default permissions set.

While certainly not elegant, it did work for me
Code:
Set-Location "C:\Windows\SystemApps\Microsoft.MicrosoftEdge_8wekyb3d8bbwe\Assets\"
Get-ChildItem | Where-Object {$_.Name -match "MicrosoftEdge(Splash|Wide|Square)"}| Where-Object {$_.Name -notmatch "^MicrosoftEdge[A-Za-z0-9._-]*-white"} | Where-Object {$_.Name -notmatch "^MicrosoftEdge[A-Za-z0-9._-]*-black"} | Rename-Item -NewName {$_.Name -replace '.png','.png.bak' }
Get-ChildItem | Where-Object {$_.Name -match "^MicrosoftEdge[A-Za-z0-9._-]*-black"} | Rename-Item -NewName {$_.Name -replace '_contrast-black.png','.png' }