This prototype robot skin came out at .4 inches thick. The five layers could be made thinner resulting in a skin about .25 inches thick. Even thinner skin might be made using conductive fabric instead of Oogoo II. The only limitation would be the thin plating on most conductive fabrics that might wear off fairly fast.
If you don't need skin that is touch sensitive everywhere, a three layer skin could be made that is only sensitive between the spacer dots.Curved Skin
The layers can be glued up on a curved form such as a pipe. For compound curves, the sheets would have to be molded on a form with the proper curves.Tile the Robot Skin
Oogoo II layers can be laminated behind a continuous sheet of Oogoo to create touch sensitive zones to give a higher resolution of touch sensitivity.Human Touch Sensitive Skin
A two layer skin of laminated Oogoo and Oogoo II can be made that is sensitive to human touch. The capacitive touch detecting inputs of a Picaxe microcontroller can be used, or you can try this circuit: https://www.instructables.com/id/Curved-Circuit-Board-Art-Make-a-Touchless-Touch-S/Touch Sensitive Clothing
Two layers of conductive rubber with spacers between, can be glued behind shirt fabric to make pressure sensitive switches for wearable electronics.Human-Like Skin
Oogoo has a smoothness and texture very similar to human skin. By varying the thickness of the layers and the pattern of the spacers, a robot skin that has the feel and resiliency of human skin could be created.Other uses
See here for another use for conductive rubber: https://www.instructables.com/id/Make-Conductive-Rubber-Transparent-stylus-iPodiP/