Admission time… I’m a secret, or perhaps ‘recovering’ lefthander. That is to say I write and use a mouse with my left hand, but apart from that I’m basically right-handed. I play guitar right-handed. If I played racquet sports or golf, I’d do it right-handed. I still rely on my left hand for detail stuff, so if I was painting a picture, I’d be left-handed, but painting a wall I’d probably use my right, or both hands equally, depending on which awkward corner I needed to get into.
Handedness doesn’t really come into cycling that much. You would think that, perhaps, which way round you ran your brakes might depend on your stronger arm. Saying that, though, would you want your front or rear brake covered by your stronger (or less prone to fatigue) arm? Regardless, brake-ness mostly follows country-specific conventions that appear to be based on which side of the road we ride on. No one has ever given a definitive answer to this, although it’s said that having your non-signalling hand covering your rear brake while turning across traffic makes sense. That, or it’s to do with bicycle pistol duelling…