We just recently finished dealing with a massive whitefly infestation in our retail greenhouse. While our methods of harsh chemical control are obviously not possible within the confines of our animal enclosures, whitefly should not be too prolific in a lightly furnished cham cage. These flies should not bother the animals themselves.
Sterlings suggestions seems sound and is worth doing. You might combined this method with yellow sticky traps used OUTSIDE the cage, and wiping the undersides of the leaves with baby wipes. With that said, I thing Sterling's spray advise should take care of your problem by itself, perhaps outside of a few stray flies hiding out around your room and the enclosure.
Of course use caution in using sticky traps, as escaped animals can result in a terrible outcome. The benefit is the flies are often attracted to yellow, as most sticky traps will be colored so.
Let us know how this issue progresses. It was an absolute nightmare dealing with them in a large retail greenhouse, as I can attest!
