It's been a long time since I've offered a drag-queenery tip. This one is for queens, girls, and unhappily hirsute men who occasionally use Nair.
I used to just goop it on my hands, then rub it on the area I wanted to depilitate. This wasn't so bad but it quickly got messy, especially when the bottle itself got covered in Nair and would start slipping around.
Now that my shoulder has a limited range of motion I've had to be inventive, and tonight -- for the first time -- I tried using an "extender," namely, a wooden spoon. I put the Nair on the back (convex) side of the spoon, then extended it to the area I wanted to depilitate, and besides being an easy way to reach out-of-the-way places it also proved to be more clean and accurate than my hands ever were.
So give it a try!
PS: If you're getting a chemical burn from the strong stuff, maybe try the mild next time, it might be all you need. Ouch!