You could replace the T-SQL in the sp_send_dbmail procedure with a call to your mail client and you should find that SQL does not know that you have bypassed SQL Mail. You could also replace the queue processing procedure for SQL mail (it uses service broker) and basically do the same thing. I would question the use of a third party mail system though. Most use SMTP for sending mail, so you may simply be bypassing SQL Mail and ending up doing the exact same thing in a less-tested way.

What mail application are you using?