I think you'll be okay NOT turning on the light at the usual time and then turning it on 12 hours later -- There are dark rainy days in nature (though there is some light, obviously). And during Sandy in the northeast, when a lot of indoor grows didn't have power for a while, I think most people's plants recovered pretty well if the lights came on within a day.
Obviously it's not ideal, but if you have to make the change that's probably the easiest way to do it. You might have to add a few days to the flowering period before harvesting, but you'll judge that from the trichomes.
Since light stress can disturb the plant and increase the chances that it will try to self-polinate, do look for signs of herming if you want to keep your bud sinsemilla.