Turn off the mail sound and then get the app named 'Boxcar.' Set it up with your e-mail account.
The point of Boxcar is to give you pop-up notifications when you get mail, but a side-benefit is that it has its own sounds when it does that. So you let Boxcar make a noise when you get mail and you can change it in there.
Sadly, you can't add your own sounds to it, but at least it has several new ones that don't sound like everyone else's iPhone on the planet.