Hi Gary,
The Blog widget itself does not yet support external links, but you could use the Recent Posts widget which does support the deactivation of the linking to the posts, then you could eliminate the "continue reading" link (either by changing its wording to none in the "customize frontend wording" option of the Settings section of your blog, or by deactivating the "blurb" option), then you could create your own link at the end of the main text using the "insert link" option of the blog post editor.
Also there would be a way involving the main blog widget, using custom fields to create a larger link or a button which would carry your external link. This field could be present at both the post list and the post page.