From my experience, this is the only time that you can be safe in entering an old bucks core area, his bedding areas that is. You are not going to hurt anything if you push him out for now. It will not take him long to come back into the same area and go back to his normal ways. Besides you have until next hunting season for him to forget about it. I have been doing this for years and this the only time of the year we actually go into the sanctuaries and we still see the same buck year after year. This is also some of the best info you can get for next years hunt. I owe alot of success to shed hunting/scouting this time of year.
I went yesterday during our "snow storm" with my dog. He found 4 sheds. One half of a 10 point, a matching 8 point, and half a shed of a 4 point. If you find sheds in an area, you can bet that buck will be there next year unless he dies between here and there.