I would not do it. Even half a drop once a day is capable of serious detox reactions and knocking a robust teenager off their feet with miserable detox symptoms.

There is a product, NZYMES® Ox-E-Drops, containing sodium chlorite 5% solution. I suppose this product will allow the animal's own digestive juices to activate the chlorite in generating clo2.
The website shows only pictures of dogs, so you may want to call them and get an opinion on using it for your bird.
http://www.nzymes.com/product-ox-e-drops.htm#SupplementFacts

At the very least you can disinfect the cage or perch with no problem. And may be ok for topical application, although some care should be used with the concentration.
There is a product called Oxyfresh [stabalized oxygen] that is used for this.

http://birdsnways.com/wisdom/ww40ev.htm
"Chlorine dioxide, a safe and effective disinfectant for pet birds and aviaries...

Without going into a technical explanation, chlorine tends to react with organic matter by attacking cell walls and creating by-products, some of which are toxic and carcinogenic; where chlorine dioxide does not affect cell walls (which is why it is safe to use around living things).

Oxyfresh makes a cleaner called Cleansing Gele' that contains chlorine dioxide. It is the easiest cleaner I have ever worked with. Spray it on, wait 5 minutes and wipe or rinse it off. The Gele' was also found to be effective as a disinfectant (5 minute contact time) by The University of Georgia's College of Veterinary Medicine. I do not have much experience with parrots, but I keep grass parakeets, and their poop is like cement! The Gele' softens the "cement" like nothing I have ever worked with.

Along with its disinfecting properties, chlorine dioxide is also a natural anti-inflamatory, making it very useful for wound treatment. Veterinarians are using a chlorine dioxide gel mixed with aloe vera to treat incisions and wounds. It's also very good as a spray for feather pickers. Stabilized chlorine dioxide mouthrinse is very good to use on neonate mouths after hand feeding to prevent leftover food from incubating gram negative bacteria and Candida."