iPhone 4s iOS 9.3 here; How to adjust the sound balance of the audio in very small db increment?
The slider control is much improved on iOS 10 - I find that once I start to drag left or right, moving my finger below the slider substantially lets me see it move in very small increments and let go precisely where I wish.

I do use newer hardware, so you might be out of luck with iPhone 4s and iOS 9 if you can't get such a small fine adjustment with either a stylus or your fingers.