Not long ago, after bathing, my (mostly) white Budgie decided to rub against a vegetable dyed wooden perch and her tummy turned orange

! The other did something similar - rubbed her wet face on a red vegetable dyed wooden block and when I first saw her I nearly had a heart attack-I thought she was bleeding! It took approximately 3 baths and at least 4 times of me misting the white one for it to fade. I couldn't wait for the orange to be gone-she looked so silly. The other one within a day had stuck her head under water & in her food dish enough times for it to come off.
Anyway, I wouldn't use soap or any of those sprays on a bird. Birds are very clean creatures and will preen and bathe sufficiently if offered cool water, mist, or wet greens. Most shampoos, soaps, and mists have some sort of chemical, dye, scent, or preservative that could be questionable/toxic.
The vet agreed completely with never using soap on a cage, just water with a tiny amount of bleach.
Yikes! I can't fathom why he would suggest using bleach. Chlorine bleach is a lung irritant and is corrosive to skin and eyes in humans. I know he is probably saying to use a tiny diluted amount, but still I would never want that in my bird's mouth/cage, and I would imagine the fumes alone could harm a bird. Disinfectants such as bleach are considered pesticides! When I was a teenager and worked in a restuarant they were fined for me accidentally using too much bleach in the dish rinse. I used 1 small capful in 20+ gallons of water -and the health dept. said that was too much for humans. I only bring this up because I hope none of the kids who frequent this forum don't read the above, use bleach and accidentally kill their bird(s).

There are soaps that are chemical, preservative, scent, and dye-free that are derived from corn or coconut and are bird safe. This is what I use on my cages and all my bird toys. I would never not wash them with (bird-safe) soap.
As for disinfecting, distilled white vinegar is safe and non-toxic. Rids approx. 99% of all bacteria. I have read others on this forum use apple cider vinegar, which supposedly does the same. I have read that a 1/2 hour soak of 50% white vinegar with 50% hydrogen peroxide (which is an oxygen bleach and completely different from chlorine bleach) followed by a thorough rinse does the job for thoroughly disinfecting bird cages and should be done every 2 weeks.