I don' t think you will be showing the deer any disrespect. Hanging them on the shed is 1 way many thousands of people choose to display their racks.

Please, do not throw them on the ground in the back of the barn or on the " pile" behind the shed. I see this much to frequently on the farms I hunt in PA and NY. They live with and around deer constantly all year round and see them as eating machines of good crops. Many of these guys love to hunt as well and it is a very strong tradition with them, but once they are in the freezer and a photo or 2 has been snapped many racks end up thrown behind the barn. No matter how hard I try and explain that just nailing that rack to the wall instead of letting it rot on the ground would be more respectful they don' t get it. I' ve even offered to do it myself.

Nothing wrong with hanging them on the shed. A good mount is expensive for some people, around here it' s about $400.