I am happy for others to correct me on this, but basically there is a very big overlap between the application of servos and stepper motors and you could use either. In your particular case a servo may be better as I would expect it to generate less heat and, since it is not stepping, to have less vibration.
In general servos only operate through 180 degrees, but that probably meets your needs. One thing I am not sure about is speed, the larger the move you are trying to make the faster the servo will try to go. You could move the servo in small increments, but that might bring back the possibility of vibration.