Blu Kote is wonderful stuff, and just fine for poultry. If you ever need to treat somewhere that spraying is too awkward, you can apply it to a paper towel or gauze first and dab it on. But yes, gloves are a must!
You might want to consider putting together a chicken first aid kit, I use a small plastic storage bin with a locking lid, and keep vet wrap, Blu Kote, Vaseline, plain triple antibiotic ointment (no pain relief), guaze pads, dedicated manicure set with tweezers, nail clippers, cuticle scissors, jar of cornstarch (to stop bleeding) syringes 1ml and 12ml 18guage needles, small bottle of ivermectin cattle pour-on, guillotine nail clippers, and pre ground up calcium tablets. And yes, GLOVES!!! Several pairs of disposable exam gloves, I keep this with several dedicated old “chicken towels” folded and tied in a garbage bag. But I also end up working with a lot of rescues. A dog crate and a cat carrier with top and front doors are also handy for isolating sick birds. (I really like the top opening, very handy if you need to work by yourself