Heya, is there a Chrome shortcut on your desktop right now?

1. Unpin the Current Chrome button from taskbar.
2. Change the Chrome's icon from the desktop shortcut.
i. Right click the desktop shortcut
ii. Click on Properties
iii. Click on Change Icon
iv. Find the Personal Icon you want
3. Pin the Chrome shortcut to the taskbar.
4. Click on Chrome, see if it uses the new personalised icon.

I just tried something like this just now, it worked for me.