I used to bleach, long long ago, in High School. I stopped in college, after getting a slight tan one spring, and having a nice stand-out bleach white mustache. Once a guy told me to shave it, I immediately went to wax. (Definitely a low point in my life with facial hair.) So after that I would never ever EVER bleach again. And you're right, it did always tingle/sting!
I have my own wax kit that I've had for about 20 years. It has it's own heater and a compartment for the wax cartridges. I do my own eyebrows and used to do my upper lip, which I get lasered now. After I'm out of this wax refill I'm going to have to find something else, they don't make them anymore. So I can't recommend one to look into, but I'll be looking. Only wanted to say it's really not that hard.
I clean the area, pat on some baby powder, put on the wax (not too hot, I blow on it first), let it harden a little (I've found if it's not cool enough the hairs won't be stuck in there), put on the strip, pull the area taunt and rip in opposite direction of hair growth. I follow up with tweezing any stragglers. Then I've been applying Burt's Bees Res-Q Ointment, it helps the area calm down.
I usually wax before bed to give the redness time to go away.
"Every mother needs a wife." - Amy Poehler, Yes Please