Mask would be good, but you'll likely have more dripping than airborne issues.
Sprayer nozzle should be held right against very close birds skin.
Wear water proof gloves, wash hands, arms, and clothing pronto.
Hmmm, those don't look like poultry mites to me....
....good pics with ruler, can't see them on the bird butt pic.
@Overo Mare @Tesumph what do you think?
If they are on the birds you still might want to treat the birds with permethrin dust.
Did you examine the birds closely for bugs...