Itching is mainly caused when the hair is shaved smooth to the skin, because it is often pulled up slightly before cutting, and then it sinks just below the skin. As it regrows, the sharp edge of the hair can irritate the skin, or even catch on the skin and start to grow under it (ie. an ingrown hair), both of which cause itching and red bumps. That tends to decrease over time as the skin gets used to it, and also varies based on shaving technique and any after-shaving products that can help the skin not be irritated as hair regrows. Yes, you can use an electric shaver. If you're using an electric shaver to shave the skin smooth, you'll likely have the same itching and irritation as you would with a razor. If you're just trimming it short so that the hair actually extends out of the skin some small distance, regrowth won't cause itching in and of itself; however, once the hair starts to get around a quarter of an inch long or so, it's still too short and stiff to flex easily and lay flat and can tend to be itchy because of how it rubs against the fabric of your clothing when you wear something. Think of two different brushes with the same thickness of bristle fibers, but one is short and the other is long: the short one will be stiffer and more abrasive while the long one will have much more flex and be softer.
Shaving or trimming of pubic hair is a matter of personal grooming preference, so ignore those who say anything negative about it. The type of shaver and the method you use is up to you, and over time you'll find what works best for you. Some people prefer dry shaving, others shave with just water, others with shaving cream or soap; some pluck, some wax, some use a chemical depilatory, and some even go as far as having laser hair removal so they never have to worry about it again.