Outside of the problems it can cause you as a seller, in that you are trusting someone else to both have the item, and send it timely, which are pitfalls of drop shipping, you have to have a profit. Have you checked to see if what you plan to sell is already on Ebay? And what the price is? Many larger, more established sellers may get a volume discount or reduced rates that you cannot hope to match. So you will be listing but not selling.
Also, some state in the listing that the item will ship from one of their warehouses. So the buyer knows up front (if they realize that this is what that means)
Most buyers do not like finding out that the item they ordered from you came from somewhere else. If you don't tell them plainly up front, they feel betrayed and take it out on your feedback. If you do tell them upfront, they may hit the back button. If they don't do either of the above, they have learned where their item came from and can go through them directly in the future.
Not saying there aren't some successful drop shippers on Ebay, but there is a lot of competition from established sellers. And the whole process of drop shipping is generally fraught with problems as this thread attests to.
As for your question as to what you would list for the shipping method, think about that.
