Well, furacin is a neon-yellow ointment available just about any livestock supply store. It's thick, creamy and anitbiotic. I've personally never had any trouble with proudflesh from it, nor the people I've suggested it to, but maybe that's just been luck. I'm a fan of it cause it sticks in place. It's about the consistency of vaseline. In fact, a vet got me started on it years ago, so I guess that's why I recommend it. Nitrofuracin is the drug name, I think and you can find brand names like "Furazone" etc.
Corona ointment has antiseptic qualities too. It's waxier, and the label even suggests using it as hoof moisturizer (but I'm not a hoof moisturizer user, myself) but it does coat the wound well and provides a temporary barrier to flies, just as the furacin does. It might even stick a little better thanks to the wax in it. I think it's pretty much more of a "natural ingredient" thing. My only dislike for it is it gets hard in cold weather so it's difficult to get out of the container.
I don't use Blu-Kote, so can't offer an opinion one way or the other.
Turnout, IME, does a lot more for healing wounds than confinement.Especially lower leg and hoof wounds, because when a horse stands around, the blood stagnates more in lower extremities. I think it's common knowledge that increased circulation means increased available oxygen, nutrients and anitbodies can reach the wound, while the debris can be carried away, and that for horses, movement equals circulation in the legs/hooves. Unless of course your horse has an unstable wound, like a broken bone, you would want to keep them from using it then...but for a surface abrasion/laceration? I'd let them go out on their usual routine.
Bandages tend to cause the tissue to "sweat" like your skin does under a band-aid, and after the initial cut, they seem to heal faster when dry. Just my experience, perhaps I'm just lucky? Plus, horses tend to pick at the bandages or otherwise scrape them off anyways, and then you have a mangled mess tangled up on there in addition to a dirty foot, yet that dirt seems to do less damage than them picking at the wound to get the bandage off. Depends on the horse for that one, though.
For the hoof part, I see a fissure at the heel wall. Is that not part of the cut?Or is that a scar? That will grow down and be a weak spot, eventually.Not something to panic over, just something I noticed and thought was part of the problem you were asking about.
Guess I should just say that if it were MY own horse, I'd continue turn out, unbandaged, and clean it every day and put some ointment on it. It's not causing lameness, so other than keeping an eye out for signs of infection, I'd not worry about it more than that. Perhaps that's not the right protocol for everyone, but it seems to work for me, with no lameness, infections or proudflesh so far.