It's fairly normal practice for the scanner to request empty stomachs before scanning if the gestation is well advanced. 12 hours without feed is no problem at all to sheep, especially if they have been on grass. It takes a long time for grass to digest through the rumen anyway,they don't have as fast a gut system as we do. If you must feed them something then maybe a little concentrates but NOT hay or straw. That will fill the rumen in the same way as grass would and so cause problems with the picture for the scanner.
If you think that legally stock can be shifted in a lorry (having been stood in the market for a whole day) for 8 hours and it causes almost no problems (the industry can't afford the problems, straight economics and welfare dictates that). Standing yours in a shed at home where there is almost no stress won't worry the girls.
All the best with the scanning, You'll be pacing like an expectant father!