The best way to deal with armpit hairs is shaving. Quick, painless, and if you do it right no ingrown hairs. Waxing and sugaring both push sweat residue, deodorant resiue and dead skin cells inot the openings of the follicles which plugs them and prevents the hair from growing -leading to ingrown hairs.
Waxing, plucking and sugaring all lead to ingrown hairs. I stopped getting them when I stopped yanking out the hair by the root. Instead shave: start by a good cleaning and scrubbing of the arm pit to ensure the skin is clean and free or dirt, sweat and anything else. Wet the entire armpit area and use a shave foam, body-wash suds, or even a bit of hair conditioner to cushion between the razor and your skin then shave. Start at the top and shave down and then reverse. Wash away any residue of the shave foam (or whatever) and dry the underarms. You can do this as part of your morning routine, every time you shower, or whenever is convenient. It's quicker and far less of a fuss and you end up with clean, smooth, hair free armpits.