Great strategy, but I really do think that would increase the stress in the flock more than just separating a hen for a small while…I have tried food coloring but not lipstick. Sometimes it worked, sometimes not. "Not working" included experiences like marking the only two hens who laid green eggs, different color for each hen, and then getting a green egg with no food coloring on it. I knew I'd marked them both, so somehow it just didn't work. I've had other times I thought I applied the food coloring the same way, and I got marked eggs from that hen for almost a week before I had to re-apply it. I never did figure it out what the difference was.
If you aren't willing or able to separate her, and don't want to throw out all the eggs, you might try using two colors: mark her vent with one color, and all the other hens' vents with the other color. If you find her egg marked, great! You can eat all the other eggs that day. But if her egg does not get marked, at least you can eat any eggs that got marked with the other color (might not be all the eggs, but should be at least some of them.)