Personally I would prefer that my lefty son would use PC mouse with his right hand. Is it worth a try or let him use his main left hand and prepare for infinitely changing of mouse button assignments?
I didn't start using a mouse until I was around 20 (yep, I'm old). I'm a lefty and suggest leaving mouse buttons alone, but physically moving the mouse to the left side of the keyboard.
Keeping the buttons in their default settings will allow him to use other computers easily. One aid to learning would be to use a simple, flattish mouse, not an ergonomic one.
And now that I'm on my PC, and not my phone...I rest both my ring and middle fingers on the left mouse button. Middle finger is also used for the scroll wheel while the forefinger is used for the right mouse button.
When he's older he can decide if he wants to relearn, or more likely, dual-learn the swapped buttons method.
As a general rule, you should teach your child to live in the actual world. That means not needing to specifically adapt anything to his left handness. He will have to live in a world of right handed people, and mostly everything is built for right hand convenience.
Things like writing, or using chopsticks are better left to his left hand, because that is his dominant one ; but things that require special adaptation (scissors, can openers, mice) won't always be readily available; so it's better he learns to do it as most people will.
Computers are usually shared at school, or for homework later on. If he can't use the mouse with his right hand, or if he is much slower than other people, his classmates will tend to not let him use the computer because he is the slow one.
And for anecdotal evidence, both my wife and older son are left handed, and both of them use their right hand for the mouse. And I just had a look in my office and out of roughly a hundred people only one is using it with his left hand, far less than the expected 10% or so.
Another option might be getting a ambidextrous (excuse my poor spelling) mouse (a mouse that can be used with both hands), on which you can create profiles and preferably with a button to easily switch between the profiles (with a button on the mouse).
This way you can do the button re-assignment with a click of a buttonon the mouse. However these kind of functions are often found on a bit of higher end mice (i.e. Steelseries Rival).
This can also be done on some Logitech mice (unsure if there's an ambidextrous one though.
Just throwing it out there ;)
First, mice may very well become obsolete by the time he grows up. Already, there's a generation of children entering school not even knowing what a mouse is. Nobody cares which hand you use on a touchscreen. The Apple Magic Touchpad is also handedness-agnostic: you use one finger to primary-click, and two fingers to secondary-click.
For that matter, you issue probably isn't which hand he mouses with (unless you are easily annoyed by having to move the mouse from one side of the keyboard to the other). The main issue is configuring the mouse to suit his left-handedness. The simple solution is: don't reconfigure it. He can just learn to use his middle finger of his left hand to primary-click and his index finger to secondary-click.
I don't recommend forcing right-hand use at this age, unless you are on a campaign to convert him to right-handedness. (That sounds psychologically harmful.) In any case, it's not that hard to learn to switch the mousing hand as an adult. I've done it myself to mitigate stress injury.
In summary, just let your kid use the mouse the way he wants. You don't have to make any configuration accommodation for him.