Oh, I'm getting a different picture here now. You were only using OE when you clicked on an email link on a website and OE opened. But, you normally accessed your mail via your web browser, i.e., as webmail, right?
Yes, you could use WLM that way, just as you did OE. But, as you know now, the full Windows Live Essentials is a large download. If you merely want an email client installed that will open when you click on an email link on a website, I'm inclined to think installing Thunderbird, as patio mentioned, might be a better option for you. The download would only be the Thunderbird email software and, therefore, would be a much smaller download.