Shifting an audio signal from 0 - 4V to -2 - 2V
Could an op-amp also be used for this, and how?


No need to use an op-amp if your signal is audio. Shifting a biased audio signal of 0 - 4 volts to an unbiased voltage requires only a RC high pass filter. It will remove the DC offset: -



You decide on the values of R and C so that the lowest frequency you wish to pass is: -

$$F_{LOW} = \dfrac{1}{2\pi RC}$$