I don't think there is a way to not have the messages stored in the stock app because it (sms pop up app) works through the stock messaging one. I have used handcent & other messaging apps & the messages always show on the stock app.
I might be wrong but, i think that is just the way it works...
Hole up, slow down wah, wait a minute. I think i just got an idea of how to do this.
Go into the messages app hit menu settings then general settings set text messages limit to be erased, set it as 0 or 1. That might work. Oops, it doesn't allow you do that, i can only be set as 10 massages plus. Maybe set it to 10 (the lowest number) and it will cut down on the clutter.