Hi Deanna,
We do the same thing. I created a completely blank Eloqua footer and use that for emails where we have our own footer. I also did the same thing for headers since we occassionally use our own for those as well.
If you're using E10, go to Assets->Component Library->Email Footer and click "New" in the upper right corner. Name your footer in the settings, make sure the footer is blank, and save it. Update your email settings to use your new blank footer and you should be good to go!
Hope that helps!
Ida