Why do you need to use an invoice? That's what email is for. If the buyer knows clearly who sold them the item is who shipped them the item, then what's the big deal? If a buyer needs an invoice shipped with the product, then pass on the cost of the increased shipping to them. Me, I either want a book fast, or I want it shipped cheap. If I get to pick, and pay accordingly, I'm happy.
I don't get the sellers who try to make a few extra bucks by overcharging on shipping. All it does is keep their bids down. Sometimes I even offer free shipping if the buyer uses Buy It Now.
If the package is insured and then damaged in transit, the invoice can be used to prove the insured value of the package.