So this is entirely a personal headcanon of mine, but I believe that Launch was raised with a very ‘traditional’ upbringing, which is why Blue Launch is so good at cooking and cleaning. It’s because her parents decided to raise her to become the ideal housewife. Blue Launch was the obedient version of Launch, and Blond Launch was the rebellious one. With that in mind, assuming that Launch was raised in the same manner, but was acknowledged as a boy instead, he was raised to do sports and business and finances by his parents to make sure he became a successful businessman and head of household.
Blue Launch still learned how to cook and clean, but this was through compassion and curiosity. He always wanted to help out with housework, even if he was told that wasn’t what he was supposed to be doing. He ends up being rather adept at cooking and cleaning, though not to the extent of his female counterpart.
Launch had his hair cut short by his parents, who wanted him to look like their standard of presentable. This meant that Launch sneezed far less, but it also meant that Blue and Blond had a lot more time as themselves.
One of the first things Blond Launch did when he ran away to be a criminal was grow out his hair. Partly as a ‘fuck you’ to his parents and partly as a way to disguise himself. As it grew out, he started sneezing far more, so he began tying it back in a ponytail with his ribbon.
Launch might be more notorious in this universe; though Blond Launch is most definitely a wanted criminal in Dragon Ball, it’s also possible that she’s not as widely known due to people being embarrassed at being threatened by a woman with a gun. People might have taken male Launch more seriously in that respect, and he might have been known more globally? (I personally can take or leave this headcanon, but it might be interesting if Man With A Gun Launch was known globally as a wanted criminal, but it’s entirely based on media sexism so…)
Fitting Launch into the Dragon Ball storyline is a little harder to do, given that Roshi wanted a ‘hot babe’, so… either we make this a universe where Roshi is attracted to men, or Krillin and Goku dress up Launch as a woman in their desperation. Alternatively, they find a new woman to bring along to Master Roshi and Launch tags along. (There’s probably a better way to fit Launch into the story but nothing else comes to mind at the moment.)
Blue Launch is able to train somewhat with Goku and Krillin, given that martial arts could have very well been part of his upbringing, though I don’t think he’d be up for Roshi’s training. Blue Launch is a little too pacifistic and Blond Launch has gun and knows how to punch, and that’s good enough for him.
No but seriously Launch being a warm up sparring buddy with Goku and Krillin.