Well, of course, it will be a perfect idea for your situation, as you are nearsighted. Generally speaking, prescription sunglasses are prescript and they are wildly used by many people who have vision problem and also want to go outside. So you can just have a try. By wearing them, they can just make you look well and also, look attractive and amazing. By the way, your eyes can be well protected by them, for sunglasses have uv protection.
I think getting a pair of prescription sunglasses is a good idea. Like ordinary sunglasses, the prescription sunglasses have the function of giving you comfortable feeling on bright and sunny days and protecting your eyes by blocking UV. Since they are prescript, they can correct your vision. So prescription sunglasses merge the benefits of prescription glasses and sunglasses. It is also very convenient and comfortable to wear prescription sunglasses when you are doing outdoor sports and driving. Moreover, prescription sunglasses with various designer brands will give you a fashionable look and more individualistic attraction.
I used to have the same thought like you and did it.Talking from my experience,I suggest you to get two pair of glasses,one is normal,the other is prescription sunglasses.Though wearing sunglasses is really cool,it not suitable for all occasions.If you are wearing a sunglasses wherever you go,that would be really strange.You could wear the glasses when you working and reading,wearing the prescription sunglasses when you go out.