This is exactly what I'm using at present, a Norelco Bodygroom.
Another option is a woman's razor, such as a Gillette Venus model. I would never shave my balls with a man's razor, meant for the face. If you're doing that it's no wonder your skin is irritated.
The correct drill is to get a woman's razor, and take a warm bubble bath. Then you do the shaving in the water. Apply shaving cream if needed; just stand up. Soaking in the warm water softens the hairs and reduces nicks.
But I find the Bodygroom easier, and it can be used in the shower. Just a bigger initial investment.