Chlorhexidine Gluconate is a wonderful product with many uses. Its a very affective wound wash, and is also a non caustic disinfectant. It has virtually no fumes, and does not need to be rinsed. Its also pretty inexpensive when diluted. What are the downsides? It has a long contact time...roughly 15-20 minutes, and its not the most effective disinfectant. However as a daily use cleaner, its top notch. It should be mixed fresh on a weekly basis. In tap water a mixture will be good for at most a couple weeks. If you use distilled, its a month. However it dilutes to 2oz per gallon, so its very easy to mix it as you use it.
When diluted properly, its mild enough that it can be used in the vicinity of the beardy...and it won't damage cage items (or stain them like iodine). There really isn't anything more to say.
If you are battling serious contagions, you'll want something more powerful. A QUAT (Quaternary Ammonium Compound) would probably be the way to go (Roccal D, Wipe Out). Alternatively you can use a 10% mixture of Ammonia...but be warned, its noxious. As far as I know, An ammonia solution is the only one known to take out Coccidia.
The defacto standard is probably a 10% bleach solution, and its very effective. However, the one thing all of these have in common is they are dangerous to your animals...so you must rinse like crazy and make sure to let the enclosure air out before putting the beardy back. This is why I prefer to use Chlorhexidine on a daily basis, and only resort to serious disinfectants once in awhile during total cage tear downs.