You won't have any problem leaving the US using either passport. They may ask to see your visa for Zambia at the check in counter as they are responsible for your flight back if you arrive in a country without proper paperwork.
I wouldn't worry about it too much. Spend more time planning all the cool things you are going to do while in Zambia!
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"My hands are on fire. Hands are on fire. Ain't got no more time for all you charlatans and liars."
- Old Man Luedecke
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