Firstly, down with the myths. Unkept hair is a sign of lack of hygiene. And that's not my personal opinion, it's logically correct. Armpit hair increases the surface area, and since one of the most active sweat zones, the hair receive lots of sweat which homes bacteria if let be. Unless you are super hygienic and take like two hot showers a day, then maybe yes.
I do suggest you don't keep it HAIRLESS. Not only is it feminine by looks of it, It's also not healthy.
Lets remind us that the armpits are different to crotch and face, and male underarms are not like women's.
The skin is very sensitive, with hyper active pores. Having said that, waxing would leave huge open, ugly pores that leave discoloration mark and allow blackheads to grow.
And shaving is bound to because redness (due to sensitivity and unevenness of the skin here), or if not that, ingrown hair over the process of time.
Women usually use hair removal creams but in your case
a, that would hurt like f***
b, no one expects you to do it and it doesn't look masculine (male beauty IMO is a subtle amount of hair, because smooth baby skin is a feminine trait).
c, guys sweat way more than girls do, and our hair grows way faster.
Best way to go about it, is to trim it with a scissor. Not only would it not because razor sharp hair like shaving does, nor would it leave huge pores or discoloration and infections like creams and waxing do. Your hair will be kept short, very hassle free to keep clean, look masculine, and you can easily work with a body spray and keep yourself fresh and odor free.
If you don't like this, then even a buzzer would do. It doesn't remove hair from the roots or trim it off too sharply, and have a cleaner cut than scissors.
It's virtually indifferent to hairless underarms. If you DO have to go for swimming or recreation, and are hence super conscious about your grooming, then you may pluck them off using a tweezer or wax them off (its alright from time to time but NOT regularly, that's the point). But for me, a buzzer easily does.
So yeah, buzzer ans scissor are the most convenient for a guy, healthiest and most comfortable in the routine. Lastly, props to you for being considerate about your hygiene and appearance. I have seen guys with disgusting bushes under their arms and it makes me avoid swim in the water they do :P
But like stubble, trust me, even chicks dig at least SOME hair on their man unless they wish to date a gay model (in which case they wouldn't date you assuming you're straight lol).