I'd have to see what the view looked like in order to see about the cell taking the user to the external URL. In terms of the selecting the whole row, instead of using Select to run the action, one option may be to run the action using a Menu.
Imagine that my Excel file has two columns, "Link to tool" and "Link to Request Access". In each row, I have a link to a tool website in the first cell, and in the second cell a link to the corresponding request access. As you see, it's just a list of URLs that I'm trying to implement in Tableau. Hope it's clear now. Thank you!