My Birmingham resurface, a procedure which is less invasive than a total hip replacement, took something along the lines of a 6 week recovery although that was some years ago and I'm a big wet. If the GP signs you out after your temporary unfit period then you're legal aren't you? Pace yourself and see how the recuperation runs. Each person really is different in recovery mode. The problem might not be whether you can instruct but rather how your new hip would cope in an emergency. You wouldn't want a dislocation in a forced landing while evacuating a small machine in a hurry.
Good luck and a speedy recovery!