I had a day at Wattisham last year, and talked to a couple of pilots who were training on the Apache.
Although this has nothing to do with left or right hand abilities, it was interesting to hear then speak about wearing a hemet with a head-up monocle lens over one eye and nothing over the other.
Try holding your hand in front of your right eye with something written on it, and read it- at the same time as focusing on something in the distance and you will see what I mean.
According to the military the visual differences are usually overcome after a time period, proving that they actually become capable of focusing both eyes differentially with the helmet on and yet normally without the helmet.
Amazing thing the human body isn't it!!