Sorry to hear about the cut.
I don't think the bandage will stay on. I had similar cut on Kiara and it certainly didn't work for me. I used Furazone (it was popular in my old barn because of the price :) ) and Corona before. They are OK, but very sticky and smelty IMO. I switched to this one Aloe Vera Base Vet Cream Horseman's Dream (Equine - Horse Health Care - Wound Care)
several years back and used it when Kiara had similar cut on her led, on her nose, on Jemma's leg just above the hoof, and Jemma's head. My neighbor also switched from furazone to this one after her OTTB had a bad cut on back and she borrowed my cream.
I usually clean the cut with the warm water, dry it out with the napkin and then put the cream on and leave it like that. My horses are also 24/7 out.