I just read your question again, and I will adjust my answer. If you take a shipment to the airport and pay for it at the airport using a personal credit card, just leave the boxes open and let them inspect the contents. Then seal it up and send it on its way.
If you accept sealed boxes from someone and ship it using your money then the person who sealed the packages has to be a "known shipper" and you must be an Indirect Air Carrier. Having a TSA Security Threat Assessment makes you an authorized agent for an IAC which means you can accept sealed shipments from known shippers on behalf of your IAC.
Anything taken from an UNknown shipper must be accompanied by a Shippers Security Endorsement. This is a signed statement from the shipper that the shipment doesn't contain any illicit materials and includes a courier with an STA number checking government issued ID on behalf of an IAC and signing it himself to validate and accept responsibility that due process has been followed.
In your case I would expect that you can take your customer's freight to the airport, have it inspected and ship it yourself without any problem. You then become the shipper in fact and can designate any consignee. You will be required to give a contact phone number and name for somebody to be notified on arrival at the destination.
Hope that helps. You can Google "TSA STA" and find a form to fill out to get your STA number.... or Your carrier can do it for you online. It costs money but I dont recall how much.
fired at you from my Droideka