Ok, I also tried and made it now to work :P

Create a script somewhere, for test purposes let's assume it's in /opt/openwebsite.sh:
What it does is just open url given as parameter in browser and return immediately (that's why "&" character is in the end, if it was not there, strangely "browser" never returns on my device... anyone have same problems?)

Don't forget to make it executable (chmod a+x /opt/openwebsite.sh). You must edit (or create) the script as root and also chmod command must me executed as root.

And now I have a working shortcut (wtf? no need to "\" before space? I thought that's required?)
Does it work for you also? Try with http://www.google.com and then change to your website address