Open Chome's Menu, tap on Bookmarks, on the bookmarks' page look for this bookmark's icon in question and have a long press on it. On the pop up menu choose Edit and and edit the URL.
Now set this changed bookmark to home screen as new shortcut for this bookmark. For to create this use the pop up menu again.
BTW, you asked for edit the URL ... so I've written on the way
... but the way that brownchm has described may be easier: Go to the website, on Chrom's menu check "Destop view", bookmark the site and add it to your home screen. Then delete the old icon.