For a simple quickscan of a random website, you can’t use the standard Fetch as Googlebot functionality without verifying a domain first. Since this is becoming more and more important, now Google is also looking to hidden layers of content, ads etcetera and you want to test smartphone robot too, you can make use of a simple workaround.
Make sure you create a simple clean HTML file on a domain you already own. In my case, I use notprovided.eu which is verified in my Google Webmaster Tools account. Within this HTML you can easily add a iframe or embed element, containing the URL you want to test with the Fetch As Google function.
Within WMT you fetch the URL which includes the iframe or embed section. This will show the external website, parsed by the selected Google Bot. Make sure the file is not blocked by robots.txt from crawling, so add a noindex tag. If you want to fetch a HTTPS url, you also need to have a HTTPS domain verified in WMT to including such an URL by making use of iframe or embed codes.