The watch is stamped II.61, but the serial number would suggest a slightly earlier date of 1959-1960, according to The Rolex Report serial number list. In any case, I always thought Oyster Perpetuals of the early 1960's have Dauphin hands. These look like later 1960's. Am I wrong?
This could become an interesting string. Let's see your 1002 and 1003's! Here is my 1002 from 1965:
My markers are quite different than yours. That's why I wonder if there was variation in hands as well.