We all know the story of the Speedmaster as the moonwatch (don't we?) but I for one never knew the existence of this: Worn by John Glenn through the Friendship 7 mission and one of the first two watches worn by American astronauts. (Scott Carpenter was wearing a Breitling Navitimer during the same mission).
If you want the first watches in space, you'd have to look to the wrists of the Soviets. What was Yuri Gagarin wearing?
Yuri Gagarin was wearing the 33mm Sturmanskie that was issued to all fighter pilot graduates in the USSR during the 50's
That theory depends on who you ask. While that watch was issued to graduating pilots, it was only issued until 1953, which is 4 years before Gagarin graduated.