If you're a natural southpaw, learn to fight southpaw. When you get really good, you can learn to fight southpaw and orthodox. You'll learn faster if you fight in your natural stance and what you learn will transfer easily.
EDIT: Sorry misread the issue thinking he was a righty who felt more comfortable as a southpaw but I'll just let the post be as me trying to say do what feels natural and not in response to your post
I don't think that's true. The "issue" of having a stronger lead hand than rear hand is often present in converted fighters but I don't think one or the other is natural.
Fighting by measuring with the weaker hand and doing damage with the rear hand is just how things developed probably because its the most natural thing to do for most fighters but so many things about fighting aren't natural that it's probably more a matter of the way you get brought up.
Cotto is a lefty and while he did sometimes switch southpaw in early fights I doubt that him being able to fight lefty as well made a big impact on his career. De La Hoya is converted. Lomachenko is converted. Chad Dawson is converted. Andre Ward is converted. Most of them have a stronger lead but that's only a weakness depending on your point of view.
The conventional way probably works best for most guys but if someone just keeps feeling like he feels more comfortable the other way around after a while then why waste time and force yourself to fight a certain way only to not fight that way in the end anyway or even worse fighting in that uncomfortable way throughout?
You learn fastest the way you feel more comfortable and for converted fighters it obviously isnt the traditional way. Why should you learn faster doing something that feels uncomfortable?
And obviously open stance fighting is different so why not learn it properly to begin with?
A fighter trying to force a style upon himself that just doesn't click with him is like those anti- gay christian camps you might get force yourself into fucking a girl but that doesn't mean you're not gay.
Fighting styles are to a big part down to each body type and personality and basically something you are born with or grow up with early on even ebfore you start training you can only change it so much without compromising the product