Ha ha brilliant, I work with young adults and it does amuse me all the mad things they do like this. Imagine getting so absorbed in shaving your pubes that you forget to empty the plughole where your mum would see! Would never laugh to their faces if they might be at all embarrassed but... soooo funny :)
Anyway, there is not necessarily any link with actual sexual activity at all, although it's quite likely at 16 that he THINKS about it all a lot. Why would he shave then? CURIOSITY! Really that is probably all. Would not worry.
Come to think of it, I grew my own armpit hair just recently for a while out of sheer curiosity. Did not leave it in the plughole when I shaved it off though, FGS.
WRT increasing the chances that your YP (does mumsnet use the YP = Young People abbreviation?) will have sex safely when/if he does have it:
Condoms are quite expensive to buy, so not a bad idea to have some in the house in a place where he will notice and know where they are, should he ever want to get his hands on any for any reason. In a bathroom cupboard or something is a little more subtle than placed deliberately in his room - just make them available generally, don't make it into a comment about his possible sexual behaviour.
Maybe make sure there is a big pile of them so he can take a couple without it being noticed at all, and remember there is more than one reason why he might take them - for friends, out of curiosity, to practice putting them on, or maybe to carry around pretending that he might need to use them even though he really doesn't :). Also any of his friends who visit might nab a few if they find them. I give out condoms to YP where I work, and I suspect that at least half who regularly get them aren't actually sexually active yet. But that's fine.
Of course the less often he washes, the less likely he is to be having any sex, if that's any comfort....