You can change the Icon using an external tool like "Resource Hacker":
But (!) the new Icon must have the exact format and size of the original icon.
The best tool to achieve this is simply by using gimp.
Export the godot (group) icon using Resource Hacker. Then edit that file with Gimp and replace all resolutions in that icon (they're in separate layers) by your own icon (resized).
When you export the new icon as ICO in Gimp you should be displayed an export dialogue (when saving) where you can define the exact format of every icon in that ico file. Choose the exact format like in the original godot file (here it was: 32-Bit, 8-Bit Alpha, no compression for every icon).
The new exported icon should now have the original filesize as the godot icon. Now use Resource Hacker to replace the icon.
Resource Hacker allows to uses scripts. So you can automate this process a bit from command line.
-addoverwrite MyGame.ico, ICONGROUP,GODOT_ICON,0
The command line/batch:
ResourceHacker.exe -script myscriptfilename.txt