My feeling is the opposite of LeoRose's here. I once had a rescue pull out all his stitches when in the care of someone else who didn't use a cone. The whole site was an ugly mess (not at all like the picture posted here). Had to take him back to the vet and get it all stitched up again. I don't think keeping a cone on a dog for a week or so is going to kill them, and it's better than dealing with an infected mess after.
I do agree about consulting the vet who did the surgery in this particular case or if that's not possible, another vet.
I do agree about consulting the vet who did the surgery in this particular case or if that's not possible, another vet.