Yes you should take your older kid out in public wearing just a diaper.
There's nothing wrong with going out in public wearing just your diaper as an older kid or even an adult.
I would take my older kids out in public wearing just a diaper or just a diaper, shirt and shoes like this Tommy Diaper Boy.
He's so cute wearing just his diaper.
When it's hot or warm out there's no need for pants or shorts over the diaper.
Wearing just a diaper feels awesome and I'm sure he'll have lots of fun.