I travelled for a living, often completing 25 to 35 round trips per year in the US and 2 or three overseas trips for nearly 30 years and never had film damaged by x-rays. Maybe I was lucky, but maybe the worries are not as bad as people think. My film of choice was Kodachrome 64 and Plus-X. If I was carrying really high speed I may have worried more, but I think you will be safe.