Let me see if I understand the problem correctly... you have a list of links to external websites that is used on your website i.e. your customers can click on them to go to the external website. You want to verify that the links are functional, they don't return 404 or Server not found, etc. Do I understand this correctly?
If this is the case I have to be honest and admit that Test Studio is not the best tool to solve this problem. Test Studio excels at functional and regression testing of your website, but not so well at testing for dead links. It can be done but easier solutions exist. The problem, as you point out, is you pretty much need to look for all possible errors that can be displayed in the browser. It would be easier if there were a simple "success" message to watch for, but you don't get that from the browser (you just get the UI displayed for that particular website... which could be hundreds depending on the left of your list).
Try doing a Google search on "Dead Link Checker". There are many products out there specifically tailored to handle this problem. If it were me (since I know how to program in .NET) I would write my own small tool from scratch that used the .NET HTTPRequest class to verify the website is connectable and the webpage can be downloaded without regard to actual content.
I hope that helps!
the Telerik team