Try treating your electric skillet exactly as if it were an oven: put your cake batter into a cake pan which will fit inside the skillet, set skillet temp at usual cake-baking temp, and preheat per your skillet instructions. The cake pan will need to stand on something in there to keep it off the bottom of the skillet; canning-jar rings work beautifully, or improvise with whatever you have around. If your skillet lid has a vent, open it; if it doesn't have a vent, set the lid slightly askew, so your cake will bake rather than steam.
I have to admit I've never done this with cake and an electric skillet, but biscuits and a cast iron skillet work fine! :D
Hope this helps. -