Well you can handle this either way ....
1. As jazz99 mentioned earlier you can just say that you are fulfilling your orders through Amazon!! (If you use their fulfillment center they always use packaging that uses the Amazon print on it) Just sent it as a gift and no receipt will be included in the package.
2. Use one of the second had sellers on Amazon and you can arrange with them however you want the item to be shipped. I personally work with a few that even would include my "advertisement materials" and use my shipping label ... All depends on how much you order with them ....
I sometimes find it really funny, that buyers on ebay pay more for a second hand good then what they would have to pay on Amazon for the same good brand new ... But let them be that way