No, you don't have an exemption. You have to obey the laws of the state you are flying in, just as you do when driving a car (you don't drive on the side you are used to - you drive on the side the local law states you drive on!)
This is the reason that differences from ICAO procedures are printed in Jeppesen Text manuals and the like. Significant differences should also be in your company's route manuals and training.