Fees are inevitable. There are 2 kinds of fees: insertion and final value fees. When an item is listed, you are charged an insertion fee based upon the item's starting price. When your item sells, you're charged a final value fee based upon what the buyer pays. Ebay does provide from time to time fee waivers to sellers during certain promotional periods. They may at that time waive either fees based on the promotion.
I think you can set a buy it now of 1 cent and cover the remaining value in shipping cost, which you can set yourself. Nobody really cares, if they are happy to pay you $5 for your Burger King baseball for example, they won't care if its 1 cent+4.99 shipping or 5.00 free shipping, its still the same $5 and will cost you the same to deliver it only from what I understand, Ebay would be charging you a percent of a penny instead of the percent of 4.99. I don't think they collect on shipping cost.