Is it ok for boys to shave their armpits?

I suppose: I find it no worse than shaving their heads, arms or legs. Removal or shaping of body hair has been a culturally defined practice that dates back through all recorded history. It has the same value to some as patterns of body art or adornment with jewelry.Patterns change over time.

Yes: It's junior's preference. Be glad he's making his own choices and that you're prepared him for independence. Many, possibly most, hollywood fitness guys shave most or all of their visible body hair nowadays. I remember my swim teammates who had upper body hair shaving it all before meets -- it was less common than nowadays, but still done by some athletes. Fashions change and this is fine.