Okay... lots of Moms will say "WHAT!" That's TOO young...!" (gasp).
Okay, next. This is the reality. SOME-many kids this age, DO smell stinky and have B.O.
Okay. Then, the conundrum is... if you don't do anything about it (ie: deodorant), then the Teacher will tell you. OR, the child can also suffer from ridicule or be ostracized by other kids, or just be shied away from because he/she "smells", and yes, other Parents probably notice too. So it's (1) a body issue and (2) a social "problem", since the child is young. (3) at this age, you want to really talk with him about it so he doesn't get "self-conscious" about it....
Okay, so check with your Pediatrician. Yes, to make sure it's "normal"... and "okay." Lots of kids now days suffer from "premature puberty." or "precocious puberty." And you want to rule that out... if it applies to you.
Now, my girl is 6 years old. SHE has arm-pit body odor already. YES, we had her checked by a "Pediatric Endocrinologist".... under recommendation by her Pediatrician. This is how I "learned" all this.
Yes, my daughter needs to use deodorant.... YES, we use "natural" types. YES... I DO NOT want to be criticized for this. It is a very personal thing, when a child is this young, and has smelly armpits. YES, we handle it appropriately. AND we had her thoroughly checked by a specialist. NO we are not making her use this willy-nilly.
Now, since your son is only 7 years old and has arm-pit smell already.... I would buy any "natural" deodorants, as many as you can afford, and then try each one. Then, see which one he is not allergic to.
There was another posting here before, about a 10-year old boy and the Mom looking for deodorant suggestions. Or, just search online for "allergy free deodorant" or other things, and you will sure to find lots of info.
All the best, and good luck,