I found some industrial molded-paper devices, which were made to protect furniture in shipping, in my alley dumpster a number of years ago. I have saved them faithfully, knowing that their time would come.
I placed the gift into the cavity inside and lightly glued the two halves together. I did this before giving any thought to what would happen next. Using occasional dots of hot glue I attached a bit of red ribbon to cover up the join of the two corners. Then I eyed the half circles along the joint and tried out a number of round things, choosing finally some water bottle caps. They are on both sides. This wrap is the same on both sides.
I already had a box of green packing peanuts lying our for the holiday shipping effort. These green beauties, though fragile, had just the right color. In went 12 peanuts, with a dab of glue. Wrap accomplished. And a wrap with a very different look and feel.