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A Rolex should be fine to fly with. Many many people fly with their Rolexes (much older than 2003) all the time.
Your watch does not use a battery.
If it is truly off by 25 minutes a week, there is something wrong. It's so far out of regulation that I'm guessing it's not just regulation and needs to be repaired by a watchmaker. Should be more like 1 minute a week.
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