Are you thinking about removing a raised cheek piece? If so make sure that by doing so you don't create a stock with too much cast. Sometimes a cheek piece gives you cast and removing it moves your face too far towards the left.
Jon;
What am I missing here? Would not removing the cheek piece move your face to the right. This seems to be compatible with your first warning of not giving it too much cast. I don't understand how removing wood from the left side of the stock can move your face left. I do agree it will change the fit so if it fits now could be detrimental to good shooting.