I use Pet Focus cleaner. This:
https://www.mangopet.com/category_s/23.htm
You can use it with the birds in the room. I use it to disinfect the floors in the aviary, walls, mesh, cage, toys, perches, as well as on a their giant apple tree branch. You don't have to rinse it off, so that's really convenient for my purposes. If I'm cleaning their toys or perches, I'll have them (the toys and perches) soak in the cleaner for 10 minutes before thoroughly rinsing them with water, but for cleaning the cage, walls, floors, giant branch hanging from the ceiling in the aviary, I don't bother rinsing with water.
With most cleaners, you need to: take the birds to a separate room, wash everything before even using the cleaner (what's the point of the cleaner if you're supposed to wash their cage before using the disinfectant?), thoroughly rinse with water, let everything air dry for an hour, then finally you can put the birds back in their enclosure. With the Pet Focus, you can buy the concentrate, figure out how much cleaner you need for X amount of water, and it'll last a couple years. You don't have to worry about rinsing all of the cleaner off their things, and you don't have to worry about fumes. The only time you'd need to worry is if you were keeping the bird in a puny, air-tight room and accidentally filled an entire bottle of the concentrated solution on the floor.
Anyways, it's almost completely odourless (it smells less than lemons or vinegar), it's non-toxic (you should still avoid spraying it all over their food), gentle (I've got some of the undiluted stuff on me before, and my skin didn't melt off), and kills pretty much every pathogen (AIDS, rabies, SARS, salmonella, MERS, flu, fungal stuff, etc.). I've used it for well over a year now, and my birds don't have any problem with me using it near them. I'm paranoid when it comes to their health and safety, so I wouldn't be using it if I didn't trust it.