I would go with the 1/16 sheeting. I can’t imagine trying to edge gluing 1/32 sheeting. Make sure you use contest grade balsa (4-7 lbs per cubic ft) for the weight and ease of sanding. Once you edge glue the sheeting, you can place it on flat surface and sand with a T-bar to thin it down a little. I have had good luck with National Balsa.
http://www.nationalbalsa.com/Aero_Light_Balsa_s/20.htm