Since this game involves operating as a team with another person while basically hugging them it works best when you can pair guests with people they are comfortable with in close contact.
Let your party guests know that you are going to have a gift wrapping contest and that they should break up into teams of two. Have a table set up with wrapping paper, scissors, clear tape, some ribbons and a small/medium sized box. You are going to need one box for each team, try to get them all the same size(or at least close to the same size). The surprise is that the teammates will stand next to each other with their inside arm around the waist of their partner so that one person will only be able to use their right hand and the other will only be able to use their left.
Set a timer for five minutes and turn the first team loose making sure that they only use their outside hand. At the end of the time set their wrapped present aside, being sure to label it with the names of the team that wrapped it and let the second team have a turn. Continue until all teams have had a chance, then bring out all of the wrapped presents and have everyone vote on a winner.