The question says it all.
Is there a way to browse for website links such that, upon selection, it'll return the URL string from the dialog?
You do not browse for website links since there is an almost infinite number (and how does your application know what they are?). Instead, you can just create a custom form with a textbox on it and sanitize the input (pass it to the
Uri constructor which will parse it for you).
As long as the ValidateNames property is false, you should be able to pull a URL out of the FileName property. You'll still have to deal with fetching the file specified in the URL on your own.