Misting is pretty safe as long as you aren't intentionally squirting the water directly into the bird's face. When tiny droplets of water are just drifting down the birds aren't going to inhale very much, and mother nature can cope with it.
I have 13 birds, and my hand can't cope with squeezing the trigger on a spray bottle long enough to get them all wet. So I take them outside in cages on a nice warm sunny day and give them a bath using the mist setting on the GARDEN HOSE!!!!!

I sweep the hose back and forth so the mist doesn't fall on any bird for more than a couple of seconds at a time, so they have opportunities to breathe mist-free air. Sometimes a bird will inhale enough water that its breathing starts to sound a little squeaky, but it dries out pretty quickly.
Some people take their birds in the shower with them, and you can buy shower perches like this one from
http://www.windycityparrot.com/Bird-Sho ... QgodMVIAGA :
Bigger birds can go directly under the shower spray, but small birds usually prefer to be off to the side where they can catch some mist but don't feel the full force of the main shower.