Hole size is not the only determinant - threads per inch(threads per centimeter) have to match. The battery caps from most Wittenauers are much finer threaded than the caps on say, a Bulova, despite having virtually the exact same pitch diameter(over the threads).
I have one of that exact same watch here....sure I can locate two of those caps...rarely do I throw them away. If only to pluck out a carefully used matching set to finish some piece off nicely.
A nice quote from a site comparing and discussing the measurment of Imperial and metric threads.
"TO PROPERLY IDENTIFY A THREAD, YOU MUST HAVE BOTH A DIAMETER MEASUREMENT AND A PITCH VALUE, OR THREAD PER INCH VALUE. Using a thread gauge(or counting) on those little short caps would be a bitch.

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