The reason those topical antiseptics are harsh to flesh is the reason they work. They kill living organisms. If the wound bled good and is clean you don't need them, if there is a lot of dirt, the trade off in damage to the wound is made in killing off the bad stuff as well.
I see what you are saying ~ but think that there is a better way. Flush the wound, I use a spray bottle on a size like the one mentioned. Blue wash if I have it (I cannot remember what this is, I want to say antimicrobial (or microbial??), am not sure. Is NOT antiseptic or antibiotic), water if I don't. Give injectable antibiotic if you are concerned with infection ~ No harm done.
If you have a big flap of skin it may dry out and die - you might want to trim it off so it doesn't catch on things and tear the original wound back open repeatedly. At least on horses, I tend to stitch skin back in place if it is clean and alive. Don't think I have ever actually seen it on a cow.
I agree ~ get rid of any skin flap. All the stiching I have done comes undone ~ not enough blood flow to site of damage, skin dies, stiches slough out. Then I have to deal with it twice. If I start stiches back into viable flesh, then the flesh puckers. Maybe I am not so good a surgeon. ;-) I would advise trimming them off.