As you are CS major, you definitely have to go for programming. I have seen people from business doing programming after few month training, so you can obviously handle it.
Now a days every employer is looking for good communication skills as key requirement. Communication is very important. However as a developer you dont have to do alot of communation as other fields like marketing.  ( depends on the company though. Some company have meetings everyday). As long as you finish your task on time, no body cares about how you talk.
In the mean time you can improve your public speaking skills. You can do few things which are scientifically proved to work:
1. record yourself on camera and practice reading a page loud ( as loud as you can). Watch the video and you will find your weakness yourself. improve on it next time.
2. prepare short poem or story and recite infront of friend or family standing not sitting.
3. watch english TV series like Big Bang Theory, etc
4. be confident about yourself.