It's not going to be easy, as you'll have to integrate with each one of these services. How about going at it a different way? For GMail (at least on Chrome) you can figure the web app as the handler for your mailto: links. With that, you can create a link that opens GMail, optionally with subject and body filled in. See RFC2368 for details, or try this link.
Most users don't have accounts on all of the web mail services you mentioned anyways, and using the mailto link allow the mail to the sent using the user's default e-mail client (may it be Outlook, or GMail) which most people prefer anyways.