I do not have any suggestions for an electric razor (I did not even know they made those for women anymore) but I have had great success with the Gillette disposable Venus razors. I have never cut myself with them or had any other of those lovely side effects.

The first time I shaved my legs I was using one of those old fashioned double sided razors. I got distracted and ended up taking a six inch strip of skin of my leg. It bleed forever. Not only did it leave an odd scar, but ever since then I would get a "nick" around that area every single time I shaved. For over 30 years I walked around with toilet paper or a bandaid on my leg every day until I found the Venus razors.