It really sounds like you might not have a whole lot of choice about removing her from the cage, whether it's with a ball, or a box, or another kind of container. Having her in the tub...with the drain well blocked, of course...as suggested above, might keep her occupied until you are done. Sometimes, what must be done, must be done.
I do want to say this though. At 2 years old, your hammy is a lovely age. I think it is just wonderful that you accept her as she is and give her the space she needs. Not every hamster is cuddley, or even wants to be touched or handled. Being able to allow your hamster that space away from humans shows real caring for a small furry soul. A "look, don't touch" hammy is not for everyone. I am just glad she has you.
{hugs}
Welcome to Hamster Central!!!