Is there any way to change the .exe and taskbar icons without modifying the .exe file itself?
For example I tried changing the icon of the Cyberpunk exe and when opening it with resource hacker it showed that it already has two other icons in that file. Is there a way to set which icon should be used without that program?

If you mean edit the icons yourself, then extract the icon's from the .exe using something like IcoFX, edit it as you want it then save it as a separate .ico file. If you mean just replace it with another icon you downloaded, then simply point the shortcut link to that .ico file instead of the .exe (right-click on Shortcut Link -> Properties -> Shortcut -> Change Icon...)

Quaint. I can't remember the last time I thought about shortcuts and icons.

If the exe contains an alternative ico natively, then all you should have to do is "change icon" in Windows and select the game exe. It should (and I say should, 'cause I haven't done this in years) let you select from the list of images the exe has contained within.

As others have kind of indicated.
Just create a shortcut to the game EXE and modify the properties of that shortcut to change what icon is used. You can then put that shortcut anywhere (i.e. Desktop) and use it to start the game.

This only changes it for the shortcut icon but not the icon in the taskbar or of the original .exe itself.
I already found out that it uses those other built in icons for the shortcut icon selection and guess those are only for that.
Changing the icon systemwide probably requires modifying the file.
Wouldn't try that in any MP game tho.

You mean dragging the new shortcut to the taskbar doesn't keep the icon you chose?

And as for the original exe ... does it really matter that much to you? It's installed "out of sight" and at least in my case I don't visit the install directories that much after installation & setup.

What Braggadar said.

And it would be crazy to change the icon inside the EXE. A lot of effort for no real purpose.

If one were real desperate, they could create another starter EXE and assign whatever icon to that, but I fail to see the need, as unless you are browsing to the game folder each time and starting the game by manually executing the game's EXE file, everywhere else you start the game from uses a shortcut, which can have any icon assigned to it. Hell, you could even create a shortcut in the game folder, that sits right next to the EXE, and use that.