Veet doesn't irritate my skin very much. I got a nasty chemical burn from Nair once, but its because I was trying to nuke a patch of stubborn hair and kept it on too long. Timing it everything and you have to be ready to flush the whole area with cool/cold water, I usually do the whole process in the shower. Also, DON'T rub the area with anything just rinse (you can use the little plastic spatula that comes with some veet formulas, but be very gentle with newly treated skin.
Watch the time, its very important, its better to have the odd patch of hair to shave afterwards than a burn. Better to underdo it than overdo it. Once you know how much time certain sensitive areas need, it gets easier though.
I divide into Zones, the top-front (around the waist line) the middle-front (further down) and the "under carriage" (think the most possible sensitive areas) the last zone needs less time. The back isn't so sensitive, so I used the same timing as I would for the top front.
One last tip, you can also use a bit of vaseline to keep and hair remover off of places that don't have hair, but might accidentally get some collateral damage.
Hope that helps, if not DM me (trying not to be too graphic here in the forum post)