But this will only create new one, then there will be two results of one app in app launcher, which is annoying.
Is there any method, that I can only change the ‘exec’ of the original .desktop file?
The google-chrome package has its desktop file at share/applications/google-chrome.desktop.
One of the ways you could confirm this desktop filename is by running:
xdg-settings get default-web-browser
Try changing the xdg.desktopEntries attribute name chrome to google-chrome.
This should ensure that your home-manager desktop entry replaces the one belonging to the google-chrome package, instead of creating an additional desktop entry with a slightly different filename.