Don't do it. I used to do it, and, even though I did not "hide" the charge in the price of my item, I was accused of it over and over and over.
Some people just will never believe you, no matter how honest you are. And they won't let up. Trust me. I had an ugly incident on another selling site because of this very issue.
Just charge the shipping and save yourself a world of nightmares and headaches.