I’ve waxed for years before getting laser and electrolysis on bikini and underarms. It didn’t increase my hair growth and didn’t make things worse. The biggest issue with this side effect is on a woman’s face and/or when the hair is originally fine. I wouldn’t worry about it for these areas. Shaving is also an option.
Btw, any method that removes hair with the root basically does the same thing and will have similar side effects, i.e. waxing, sugaring, threading, plucking, etc. Shaving and a depilatory only removes the part of the hair that’s above the skin’s surface, so it’s technically just clipping it. It doesn’t affect the hair in any way. So that’s always an option.