I would AT LEAST use a soft cervical collar which you can get at a pharmacy or health supply store. They are not very expensive, and work quite well. I use mine when my herniated disc acts up and it works great. I think I would feel safer if I were you, and I'd use it. I think he's a little less cautious than most doctors, cause you CAN get bumped or jolted, etc., very easily, even at home.
DO NOT WEAR IT ALL DAY. Your neck muscles will get too weak. Wear it perhaps 3 hours, and take it off. Then back on for 3, and take it off, etc. Just be careful while it's off. But just don't wear it all day, ok? That's really important.
I'm sure it will make you feel more at ease. Take care . Hugs, Lee