Check whether the store accepts non US credit cards when you checkout from their site. Some stores accept certain international credit cards but will only ship to a US address.
Search the web for companies providing pre-paid or top-up credit cards. Buy one and have it registered to your Express Delivery, LLC shipping address.
You can buy virtual gift cards of various values from many department stores with your non US credit card. Remember to provide your Express Delivery, LLC US shipping address when completing the store's registration
Click here for an example of a virtual gift card.
An increasing number of shops are accepting PayPal.
Click here for a list.
Many shops will let you pay by phone with a non US credit card so long as you have a US shipping address.
Click here for an example. Read the section at the bottom of the page - Need Assistance.