believe it or not....the underarm odor, caused by bacteria, could be "feeding" off of the soap he is using...i looked this up because i have always had trouble with this myself, i wanted to use natural products, but nothing was strong enough...
i read about it online...many people wrote in advising to stop using soap....just water.....after bathing....i have used all of the following as substitutes for deoderant with good results:
lime juice (applied with a cotton ball) and then baking soda
also tried
vodka from a small spray bottol
and recently, i began using that deodorant mineral salt spray or rock that you can find at whole food stores (this works wonders on stopping stinky foot odor if applied before wearing shoes or sandals)
this may sound odd to you, but the alcohol kills the bacteria....
since your son is so young, i think these options are better than the chemicals you find in deodorant....
i know it sounds crazy....but i don't have trouble with odor any more...and i don't worry about the chemicals that are in most deodorants out there.....
good luck!